re1tbw3

Description: tbw-ax3 rederived from merco2 . (Contributed by Anthony Hart, 16-Aug-2011) (Proof modification is discouraged.) (New usage is discouraged.)

		Ref	Expression
	Assertion	re1tbw3	$⊢ ((φ \to ψ) \to φ) \to φ$

Proof

Step	Hyp	Ref	Expression
1		mercolem2	$⊢ ((φ \to φ) \to φ) \to (φ \to (φ \to φ))$
2		mercolem2	$⊢ ((φ \to ψ) \to φ) \to ((((φ \to φ) \to φ) \to (φ \to (φ \to φ))) \to (((φ \to ψ) \to φ) \to φ))$
3		mercolem6	$⊢ (((φ \to ψ) \to φ) \to ((((φ \to φ) \to φ) \to (φ \to (φ \to φ))) \to (((φ \to ψ) \to φ) \to φ))) \to ((((φ \to φ) \to φ) \to (φ \to (φ \to φ))) \to (((φ \to ψ) \to φ) \to φ))$
4	2 3	ax-mp	$⊢ (((φ \to φ) \to φ) \to (φ \to (φ \to φ))) \to (((φ \to ψ) \to φ) \to φ)$
5	1 4	ax-mp	$⊢ ((φ \to ψ) \to φ) \to φ$

Metamath Proof Explorer

Theorem re1tbw3

Proof