Metamath Proof Explorer


Theorem bj-cbvexivw

Description: Change bound variable. This is to cbvexvw what cbvalivw is to cbvalvw . TODO: move after cbvalivw . (Contributed by BJ, 17-Mar-2020)

Ref Expression
Hypothesis bj-cbvexivw.1
|- ( y = x -> ( ph -> ps ) )
Assertion bj-cbvexivw
|- ( E. x ph -> E. y ps )

Proof

Step Hyp Ref Expression
1 bj-cbvexivw.1
 |-  ( y = x -> ( ph -> ps ) )
2 ax5e
 |-  ( E. x E. y ps -> E. y ps )
3 ax-5
 |-  ( ph -> A. y ph )
4 2 3 1 bj-cbvexiw
 |-  ( E. x ph -> E. y ps )