Metamath Proof Explorer


Theorem bj-ceqsaltv

Description: Version of bj-ceqsalt with a disjoint variable condition on x , V , removing dependency on df-sb and df-clab . Prefer its use over bj-ceqsalt when sufficient (in particular when V is substituted for _V ). (Contributed by BJ, 16-Jun-2019) (Proof modification is discouraged.)

Ref Expression
Assertion bj-ceqsaltv x ψ x x = A φ ψ A V x x = A φ ψ

Proof

Step Hyp Ref Expression
1 elissetv A V x x = A
2 1 3anim3i x ψ x x = A φ ψ A V x ψ x x = A φ ψ x x = A
3 bj-ceqsalt0 x ψ x x = A φ ψ x x = A x x = A φ ψ
4 2 3 syl x ψ x x = A φ ψ A V x x = A φ ψ