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Metamath Proof Explorer

Theorem aecoms

Description: A commutation rule for identical variable specifiers. Usage of this theorem is discouraged because it depends on ax-13 . (Contributed by NM, 10-May-1993) (New usage is discouraged.)

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

Proof

Step	Hyp	Ref	Expression
1		aecoms.1	$⊢ \forall x x = y \to φ$
2		aecom	$⊢ \forall y y = x \leftrightarrow \forall x x = y$
3	2 1	sylbi	$⊢ \forall y y = x \to φ$