Theorem frege36

Description: The case in which ps is denied, -. ph is affirmed, and ph is affirmed does not occur. If ph occurs, then (at least) one of the two, ph or ps , takes place (no matter what ps might be). Identical to pm2.24 . Proposition 36 of Frege1879 p. 45. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

	Ref	Expression
Assertion	frege36	⊢ ( 𝜑 → ( ¬ 𝜑 → 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		ax-frege1	⊢ ( 𝜑 → ( ¬ 𝜓 → 𝜑 ) )
2		frege34	⊢ ( ( 𝜑 → ( ¬ 𝜓 → 𝜑 ) ) → ( 𝜑 → ( ¬ 𝜑 → 𝜓 ) ) )
3	1 2	ax-mp	⊢ ( 𝜑 → ( ¬ 𝜑 → 𝜓 ) )