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Metamath Proof Explorer

Theorem sbequ5

Description: Substitution does not change an identical variable specifier. Usage of this theorem is discouraged because it depends on ax-13 . (Contributed by NM, 15-May-1993) (New usage is discouraged.)

		Ref	Expression
	Assertion	sbequ5	$⊢ [w/ z] \forall x x = y \leftrightarrow \forall x x = y$

Proof

Step	Hyp	Ref	Expression
1		nfae	$⊢ Ⅎ z \forall x x = y$
2	1	sbf	$⊢ [w/ z] \forall x x = y \leftrightarrow \forall x x = y$