Metamath Proof Explorer


Theorem bj-issetiv

Description: Version of bj-isseti with a disjoint variable condition on x , V . This proof uses only df-ex , ax-gen , ax-4 and df-clel on top of propositional calculus. Prefer its use over bj-isseti when sufficient (in particular when V is substituted for _V ). (Contributed by BJ, 14-Sep-2019) (Proof modification is discouraged.)

Ref Expression
Hypothesis bj-issetiv.1
|- A e. V
Assertion bj-issetiv
|- E. x x = A

Proof

Step Hyp Ref Expression
1 bj-issetiv.1
 |-  A e. V
2 elissetv
 |-  ( A e. V -> E. x x = A )
3 1 2 ax-mp
 |-  E. x x = A