Theorem chvarv

Description: Implicit substitution of y for x into a theorem. Usage of this theorem is discouraged because it depends on ax-13 . Use the weaker chvarvv if possible. (Contributed by NM, 20-Apr-1994) (Proof shortened by Wolf Lammen, 22-Apr-2018) (New usage is discouraged.)

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

Proof

Step	Hyp	Ref	Expression
1		chvarv.1	$$⊢x=y\to \left(\phi \leftrightarrow \psi \right)$$
2		chvarv.2	$$⊢\phi$$
3		nfv	$$⊢Ⅎx\psi$$
4	3 1 2	chvar	$$⊢\psi$$