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Metamath Proof Explorer

Theorem chvarvv

Description: Implicit substitution of y for x into a theorem. Version of chvarv with a disjoint variable condition, which does not require ax-13 . (Contributed by NM, 20-Apr-1994) (Revised by BJ, 31-May-2019)

	Ref	Expression
Hypotheses	chvarvv.1	$⊢ x = y \to (φ \leftrightarrow ψ)$
	chvarvv.2	$⊢ φ$
Assertion	chvarvv	$⊢ ψ$

Proof

Step	Hyp	Ref	Expression
1		chvarvv.1	$⊢ x = y \to (φ \leftrightarrow ψ)$
2		chvarvv.2	$⊢ φ$
3	1	spvv	$⊢ \forall x φ \to ψ$
4	3 2	mpg	$⊢ ψ$