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	$⊢ φ \to ((ψ \to (ψ \to χ)) \to (ψ \to χ))$

Proof

Step	Hyp	Ref	Expression
1		merco1lem6	$⊢ (ψ \to (ψ \to χ)) \to ((ψ \to (ψ \to χ)) \to (ψ \to χ))$
2		merco1lem6	$⊢ ((ψ \to (ψ \to χ)) \to ((ψ \to (ψ \to χ)) \to (ψ \to χ))) \to (φ \to ((ψ \to (ψ \to χ)) \to (ψ \to χ)))$
3	1 2	ax-mp	$⊢ φ \to ((ψ \to (ψ \to χ)) \to (ψ \to χ))$