Actually that is false
Mihawk was testing Whitebeard because he said "True Distance between that man and us seems rather small", that is the exact word for word translation and to test his theory he was inviting Whitebeard to a fight with casual nameless one handed stanceless Hakiless slash not meant to cut diamond.
I mean lets dive deeper into that. Do you think Zoro can cut Jozu with his conqueror's Haki? If not just how much more durable than Kaido and Lunara Mode King (more durable than Kaido) is Jozu?
Emperor level Law? Being Emperor level isn't exactly impressive and Law for the most part was portrayed as Zoro's minion, someone categorically weaker than Roof Top version of Zoro. He doesn't even compare to current Zoro, he would get instantly fodderized.
But anyways I am providing too much information for your limited neurological prowess to handle so I will just narrow it down.
Kinneon got hit point blank by serious Kaido's Conqueror's Haki attack and he survived
Just where exactly is Law saving him?
This Kinnemon is far far less durable than Punk Hazard Dragon who Zoro killed
So then Kaido's attacks are weaker than Punk Hazard Zoro.
Just how would he compete with Mihawk?
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Is it at least reasonable to say, even if you disagree, that Mihawk is on a whole different level than Emperors?
Like at worst he might be comparable to Emperors but after chapter 1058 a case can be made for him being on a different level as well. Is that a fair assertion?