Metamath Proof Explorer


Theorem bj-cbvexim

Description: A lemma used to prove bj-cbvex in a weak axiomatization. (Contributed by BJ, 12-Mar-2023) (Proof modification is discouraged.)

Ref Expression
Assertion bj-cbvexim xyχxyχφψxφyψ

Proof

Step Hyp Ref Expression
1 ax5e xyψyψ
2 ax-5 φyφ
3 2 ax-gen xφyφ
4 bj-cbveximt xyχxyχφψxφyφxyψyψxφyψ
5 4 com3l xyχφψxφyφxyχxyψyψxφyψ
6 5 com14 xyψyψxφyφxyχxyχφψxφyψ
7 1 3 6 mp2 xyχxyχφψxφyψ