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Metamath Proof Explorer

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 -> ( ph -> ps ) )
Assertion spimevw 
|- ( ph -> E. x ps )

Proof

Step Hyp Ref Expression
1 spimevw.1 
 |-  ( x = y -> ( ph -> ps ) )
2 ax-5 
 |-  ( ph -> A. x ph )
3 2 1 spimew 
 |-  ( ph -> E. x ps )