Theorem spimev

Description: Distinct-variable version of spime . (Contributed by NM, 10-Jan-1993) Usage of this theorem is discouraged because it depends on ax-13 . Use spimevw instead. (New usage is discouraged.)

	Ref	Expression
Hypothesis	spimev.1	$$⊢x=y\to \left(\phi \to \psi \right)$$
Assertion	spimev	$$⊢\phi \to \exists x\psi$$

Proof

Step	Hyp	Ref	Expression
1		spimev.1	$$⊢x=y\to \left(\phi \to \psi \right)$$
2		nfv	$$⊢Ⅎx\phi$$
3	2 1	spime	$$⊢\phi \to \exists x\psi$$