Theorem chvarfv

Description: Implicit substitution of y for x into a theorem. Version of chvar with a disjoint variable condition, which does not require ax-13 . (Contributed by Raph Levien, 9-Jul-2003) (Revised by BJ, 31-May-2019)

	Ref	Expression
Hypotheses	chvarfv.nf	$$⊢Ⅎx\psi$$
	chvarfv.1	$$⊢x=y\to \left(\phi \leftrightarrow \psi \right)$$
	chvarfv.2	$$⊢\phi$$
Assertion	chvarfv	$$⊢\psi$$

Proof

Step	Hyp	Ref	Expression
1		chvarfv.nf	$$⊢Ⅎx\psi$$
2		chvarfv.1	$$⊢x=y\to \left(\phi \leftrightarrow \psi \right)$$
3		chvarfv.2	$$⊢\phi$$
4	2	biimpd	$$⊢x=y\to \left(\phi \to \psi \right)$$
5	1 4	spimfv	$$⊢\forall x\phi \to \psi$$
6	5 3	mpg	$$⊢\psi$$