Metamath Proof Explorer


Theorem gencbvex2

Description: Restatement of gencbvex with weaker hypotheses. (Contributed by Jeff Hankins, 6-Dec-2006)

Ref Expression
Hypotheses gencbvex2.1 A V
gencbvex2.2 A = y φ ψ
gencbvex2.3 A = y χ θ
gencbvex2.4 θ x χ A = y
Assertion gencbvex2 x χ φ y θ ψ

Proof

Step Hyp Ref Expression
1 gencbvex2.1 A V
2 gencbvex2.2 A = y φ ψ
3 gencbvex2.3 A = y χ θ
4 gencbvex2.4 θ x χ A = y
5 3 biimpac χ A = y θ
6 5 exlimiv x χ A = y θ
7 4 6 impbii θ x χ A = y
8 1 2 3 7 gencbvex x χ φ y θ ψ