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	$$⊢x=y\to \left(\phi \leftrightarrow \psi \right)$$
	chvarvv.2	$$⊢\phi$$
Assertion	chvarvv	$$⊢\psi$$

Proof

Step	Hyp	Ref	Expression
1		chvarvv.1	$$⊢x=y\to \left(\phi \leftrightarrow \psi \right)$$
2		chvarvv.2	$$⊢\phi$$
3	1	spvv	$$⊢\forall x\phi \to \psi$$
4	3 2	mpg	$$⊢\psi$$