Metamath Proof Explorer


Theorem ceqsexv2dOLD

Description: Obsolete version of ceqsexv2d as of 5-Jun-2025. (Contributed by Thierry Arnoux, 10-Sep-2016) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses ceqsexv2dOLD.1
|- A e. _V
ceqsexv2dOLD.2
|- ( x = A -> ( ph <-> ps ) )
ceqsexv2dOLD.3
|- ps
Assertion ceqsexv2dOLD
|- E. x ph

Proof

Step Hyp Ref Expression
1 ceqsexv2dOLD.1
 |-  A e. _V
2 ceqsexv2dOLD.2
 |-  ( x = A -> ( ph <-> ps ) )
3 ceqsexv2dOLD.3
 |-  ps
4 1 2 ceqsexv
 |-  ( E. x ( x = A /\ ph ) <-> ps )
5 4 biimpri
 |-  ( ps -> E. x ( x = A /\ ph ) )
6 exsimpr
 |-  ( E. x ( x = A /\ ph ) -> E. x ph )
7 3 5 6 mp2b
 |-  E. x ph