Metamath Proof Explorer


Theorem ceqsexgv

Description: Elimination of an existential quantifier, using implicit substitution. (Contributed by NM, 29-Dec-1996) Drop ax-10 and ax-12 . (Revised by Gino Giotto, 1-Dec-2023)

Ref Expression
Hypothesis ceqsexgv.1 x=Aφψ
Assertion ceqsexgv AVxx=Aφψ

Proof

Step Hyp Ref Expression
1 ceqsexgv.1 x=Aφψ
2 id x=Ax=A
3 2 1 cgsexg AVxx=Aφψ