Theorem minimp-ax1

Description: Derivation of ax-1 from ax-mp and minimp . (Contributed by BJ, 4-Apr-2021) (Proof modification is discouraged.) (New usage is discouraged.)

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

Proof

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