This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem naecoms

Description: A commutation rule for distinct variable specifiers. Usage of this theorem is discouraged because it depends on ax-13 . (Contributed by NM, 2-Jan-2002) (New usage is discouraged.)

		Ref	Expression
	Hypothesis	naecoms.1	$⊢ \neg \forall x x = y \to φ$
	Assertion	naecoms	$⊢ \neg \forall y y = x \to φ$

Proof

Step	Hyp	Ref	Expression
1		naecoms.1	$⊢ \neg \forall x x = y \to φ$
2		aecom	$⊢ \forall x x = y \leftrightarrow \forall y y = x$
3	2 1	sylnbir	$⊢ \neg \forall y y = x \to φ$