Metamath Proof Explorer


Theorem bj-cbvex4vv

Description: Version of cbvex4v with a disjoint variable condition, which does not require ax-13 . (Contributed by BJ, 16-Jun-2019) (Proof modification is discouraged.)

Ref Expression
Hypotheses bj-cbvex4vv.1 x = v y = u φ ψ
bj-cbvex4vv.2 z = f w = g ψ χ
Assertion bj-cbvex4vv x y z w φ v u f g χ

Proof

Step Hyp Ref Expression
1 bj-cbvex4vv.1 x = v y = u φ ψ
2 bj-cbvex4vv.2 z = f w = g ψ χ
3 1 2exbidv x = v y = u z w φ z w ψ
4 3 cbvex2vw x y z w φ v u z w ψ
5 2 cbvex2vw z w ψ f g χ
6 5 2exbii v u z w ψ v u f g χ
7 4 6 bitri x y z w φ v u f g χ