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Metamath Proof Explorer

Theorem retbwax3

Description: tbw-ax3 rederived from merco1 . (Contributed by Anthony Hart, 17-Sep-2011) (Proof modification is discouraged.) (New usage is discouraged.)

		Ref	Expression
	Assertion	retbwax3	$⊢ ((φ \to ψ) \to φ) \to φ$

Proof

Step	Hyp	Ref	Expression
1		retbwax2	$⊢ φ \to (φ \to φ)$
2		merco1lem7	$⊢ (φ \to (φ \to φ)) \to (((φ \to ψ) \to φ) \to φ)$
3	1 2	ax-mp	$⊢ ((φ \to ψ) \to φ) \to φ$