Metamath Proof Explorer

Theorem adh-minimp-ax2-lem4

Description: Fourth lemma for the derivation of ax-2 from adh-minimp and ax-mp . Polish prefix notation: CpCCqCprCqr . (Contributed by ADH, 10-Nov-2023) (Proof modification is discouraged.) (New usage is discouraged.)

		Ref	Expression
	Assertion	adh-minimp-ax2-lem4	$⊢ φ \to ((ψ \to (φ \to χ)) \to (ψ \to χ))$

Proof

Step	Hyp	Ref	Expression
1		adh-minimp-ax2c	$⊢ (ψ \to φ) \to ((ψ \to (φ \to χ)) \to (ψ \to χ))$
2		adh-minimp-sylsimp	$⊢ ((ψ \to φ) \to ((ψ \to (φ \to χ)) \to (ψ \to χ))) \to (φ \to ((ψ \to (φ \to χ)) \to (ψ \to χ)))$
3	1 2	ax-mp	$⊢ φ \to ((ψ \to (φ \to χ)) \to (ψ \to χ))$