(spoilers all) Combat prowess in the far, far north

I've seen a number of people talk about Mance Rayder's combat prowess and put him alongside the likes of Jaime Lannister, Barristan Selmy, the brothers Clegane, Bronn and even Arthur Dayne.

I cannot find supporting evidence of these claims in the text. I've been searching through ASOS trying to find lines claiming him as a great warrior and I come up empty handed.

Note that I say "great warrior" and by this I specifically mean armed combat. I'm not referring to his abilities as a commander, strategist or tactician. I speak purely about his ability to go toe-to-toe with his foes.

I did find a few relevant quotes regarding his combat skill.

When Jon first meets Mance, Tormund Giantsbane (admittedly, a braggart of extreme proportions), says of Mance:

He grinned at Jon. “See, lad, that’s why he’s king and I’m not. I can outdrink, outfight, and outsing him, and my member’s thrice the size o’ his, but Mance has cunning. He was raised a crow, you know, and the crow’s a tricksy bird.”

In another Jon chapter, he thinks about Mance's history and how he formed the wildlings into a cohesive force. But while he speaks of Mance winning some groups with "the edge of his sword" that is a vague statement that could mean through military tactics just as easily as through single combat.

Mance had spent years assembling this vast plodding host, talking to this clan mother and that magnar, winning one village with sweet words and another with a song and a third with the edge of his sword...

Later on, Mance threatens Jon, but while Mance is confident that he can deal with Jon, that is a far cry from any proof that he is on par with the warriors listed at the start.

“Reach up for that bastard sword and I’ll have your bastard head off before it clears the scabbard,” said Mance. “I am fast losing patience with you, crow.”

As Jon goes to talk to Mance near the end (with the plan to kill him), he thinks about the difficulty of the task. But for Jon to think it's difficult to kill Mance could mean that Mance would have people around him protecting him, not that Mance is this good in single combat.

He flexed his sword hand, as Maester Aemon had taught him. The habit had become part of him, and he would need his fingers to be limber to have even half a chance of murdering Mance Rayder.

A bit later, he thinks about his impending death with this suicide mission. This statement could refer to an execution just as easily as a fight.

Nor would his death be quick, unless it came on the end of Mance’s sword.

In the end... nothing indicates Mance is the kind of warrior I have often seen him stated to be. He's a good commander, a good leader, a good musician and probably a good man. He's a competent warrior who can hold his own, for sure. But that doesn't put him in the pantheon with the likes of Barristan the Bold, the Kingslayer or the Sword of the Morning.

What evidence is there that Mance is a top tier warrior?