Metamath Proof Explorer

Theorem merco1lem5

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	merco1lem5	$⊢ (((φ \to ⊥) \to χ) \to τ) \to (φ \to τ)$

Proof

Step	Hyp	Ref	Expression
1		merco1lem4	$⊢ (((τ \to φ) \to (φ \to ⊥)) \to χ) \to ((φ \to ⊥) \to χ)$
2		merco1	$⊢ ((((τ \to φ) \to (φ \to ⊥)) \to χ) \to ((φ \to ⊥) \to χ)) \to ((((φ \to ⊥) \to χ) \to τ) \to (φ \to τ))$
3	1 2	ax-mp	$⊢ (((φ \to ⊥) \to χ) \to τ) \to (φ \to τ)$