Theorem chvar

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 chvarfv if possible. (Contributed by Raph Levien, 9-Jul-2003) (Revised by Mario Carneiro, 3-Oct-2016) (New usage is discouraged.)

	Ref	Expression
Hypotheses	chvar.1	$$⊢Ⅎx\psi$$
	chvar.2	$$⊢x=y\to \left(\phi \leftrightarrow \psi \right)$$
	chvar.3	$$⊢\phi$$
Assertion	chvar	$$⊢\psi$$

Proof

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