Metamath Proof Explorer

Theorem merco1lem9

Description: Used to rederive the Tarski-Bernays-Wajsberg axioms from merco1 . (Contributed by Anthony Hart, 18-Sep-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Assertion merco1lem9 ⊢ φ → φ → ψ → φ → ψ

Proof

Step Hyp Ref Expression
1 merco1lem8 ⊢ ⊥ → φ → φ → φ → ψ → φ → ψ
2 merco1lem8 ⊢ ⊥ → φ → φ → φ → ψ → φ → ψ → φ → φ → ψ → φ → ψ
3 1 2 ax-mp ⊢ φ → φ → ψ → φ → ψ