Metamath Proof Explorer

Theorem merco1lem8

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 merco1lem8 ⊢ φ → ψ → ψ → χ → ψ → χ

Proof

Step Hyp Ref Expression
1 merco1lem6 ⊢ ψ → ψ → χ → ψ → ψ → χ → ψ → χ
2 merco1lem6 ⊢ ψ → ψ → χ → ψ → ψ → χ → ψ → χ → φ → ψ → ψ → χ → ψ → χ
3 1 2 ax-mp ⊢ φ → ψ → ψ → χ → ψ → χ