Theorem frege33

Description: If ph or ps takes place, then ps or ph takes place. Identical to con1 . Proposition 33 of Frege1879 p. 44. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

	Ref	Expression
Assertion	frege33	⊢ ( ( ¬ 𝜑 → 𝜓 ) → ( ¬ 𝜓 → 𝜑 ) )

Proof

Step	Hyp	Ref	Expression
1		ax-frege28	⊢ ( ( ¬ 𝜑 → 𝜓 ) → ( ¬ 𝜓 → ¬ ¬ 𝜑 ) )
2		frege32	⊢ ( ( ( ¬ 𝜑 → 𝜓 ) → ( ¬ 𝜓 → ¬ ¬ 𝜑 ) ) → ( ( ¬ 𝜑 → 𝜓 ) → ( ¬ 𝜓 → 𝜑 ) ) )
3	1 2	ax-mp	⊢ ( ( ¬ 𝜑 → 𝜓 ) → ( ¬ 𝜓 → 𝜑 ) )