Metamath Proof Explorer


Theorem merco1lem6

Description: Used to rederive the Tarski-Bernays-Wajsberg axioms from merco1 . (Contributed by Anthony Hart, 17-Sep-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Assertion merco1lem6 φφψχφψ

Proof

Step Hyp Ref Expression
1 merco1lem5 φψχφψχ
2 merco1lem3 φψχφψχφψχφψχ
3 1 2 ax-mp φψχφψχ
4 merco1lem5 φψχφψχφψφψχ
5 3 4 ax-mp φψφψχ
6 merco1lem3 φψφψχφψχφ
7 5 6 ax-mp φψχφ
8 merco1 φψχφφφψχφψ
9 7 8 ax-mp φφψχφψ