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Metamath Proof Explorer

Theorem naev

Description: If some set variables can assume different values, then any two distinct set variables cannot always be the same. (Contributed by Wolf Lammen, 10-Aug-2019)

		Ref	Expression
	Assertion	naev	$⊢ \neg \forall x x = y \to \neg \forall u u = v$

Proof

Step	Hyp	Ref	Expression
1		aev	$⊢ \forall u u = v \to \forall x x = y$
2	1	con3i	$⊢ \neg \forall x x = y \to \neg \forall u u = v$