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	⊢ ( 𝜑 → ( 𝜓 → 𝜑 ) )

Proof

Step	Hyp	Ref	Expression
1		adh-minimp-sylsimp	⊢ ( ( ( 𝜑 → 𝜓 ) → 𝜑 ) → ( 𝜓 → 𝜑 ) )
2		adh-minimp-sylsimp	⊢ ( ( ( ( 𝜑 → 𝜓 ) → 𝜑 ) → ( 𝜓 → 𝜑 ) ) → ( 𝜑 → ( 𝜓 → 𝜑 ) ) )
3	1 2	ax-mp	⊢ ( 𝜑 → ( 𝜓 → 𝜑 ) )