Theorem frege42

Description: Not not id . Proposition 42 of Frege1879 p. 47. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

	Ref	Expression
Assertion	frege42	$$⊢\neg \neg \left(\phi \to \phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		frege27	$$⊢\phi \to \phi$$
2		ax-frege41	$$⊢\left(\phi \to \phi \right)\to \neg \neg \left(\phi \to \phi \right)$$
3	1 2	ax-mp	$$⊢\neg \neg \left(\phi \to \phi \right)$$