Theorem adh-minimp-ax1

Description: Derivation of ax-1 from adh-minimp and ax-mp . Polish prefix notation: CpCqp . (Contributed by BJ, 4-Apr-2021) (Revised by ADH, 10-Nov-2023) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	adh-minimp-ax1	$$⊢\phi \to \left(\psi \to \phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		adh-minimp-sylsimp	$$⊢\left(\left(\phi \to \psi \right)\to \phi \right)\to \left(\psi \to \phi \right)$$
2		adh-minimp-sylsimp	$$⊢\left(\left(\left(\phi \to \psi \right)\to \phi \right)\to \left(\psi \to \phi \right)\right)\to \left(\phi \to \left(\psi \to \phi \right)\right)$$
3	1 2	ax-mp	$$⊢\phi \to \left(\psi \to \phi \right)$$