Metamath Proof Explorer

Theorem merco1lem15

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	merco1lem15	$⊢ (φ \to ψ) \to (φ \to (χ \to ψ))$

Proof

Step	Hyp	Ref	Expression
1		merco1lem14	$⊢ (((φ \to ψ) \to ψ) \to (χ \to ψ)) \to (φ \to (χ \to ψ))$
2		merco1lem13	$⊢ ((((φ \to ψ) \to ψ) \to (χ \to ψ)) \to (φ \to (χ \to ψ))) \to ((φ \to ψ) \to (φ \to (χ \to ψ)))$
3	1 2	ax-mp	$⊢ (φ \to ψ) \to (φ \to (χ \to ψ))$