Theorem frege43

Description: If there is a choice only between ph and ph , then ph takes place. Identical to pm2.18 . Proposition 43 of Frege1879 p. 47. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

	Ref	Expression
Assertion	frege43	$$⊢\left(\neg \phi \to \phi \right)\to \phi$$

Proof

Step	Hyp	Ref	Expression
1		frege42	$$⊢\neg \neg \left(\phi \to \phi \right)$$
2		frege40	$$⊢\neg \neg \left(\phi \to \phi \right)\to \left(\left(\neg \phi \to \phi \right)\to \phi \right)$$
3	1 2	ax-mp	$$⊢\left(\neg \phi \to \phi \right)\to \phi$$