Theorem spimevw

Description: Existential introduction, using implicit substitution. This is to spimew what spimvw is to spimw . Version of spimev and spimefv with an additional disjoint variable condition, using only Tarski's FOL axiom schemes. (Contributed by NM, 10-Jan-1993) (Revised by BJ, 17-Mar-2020)

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

Proof

Step	Hyp	Ref	Expression
1		spimevw.1	$$⊢x=y\to \left(\phi \to \psi \right)$$
2		ax-5	$$⊢\phi \to \forall x\phi$$
3	2 1	spimew	$$⊢\phi \to \exists x\psi$$