Theorem frege27

Description: We cannot (at the same time) affirm ph and deny ph . Identical to id . Proposition 27 of Frege1879 p. 43. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

	Ref	Expression
Assertion	frege27	$$⊢\phi \to \phi$$

Proof

Step	Hyp	Ref	Expression
1		ax-frege1	$$⊢\phi \to \left(\psi \to \phi \right)$$
2		frege26	$$⊢\left(\phi \to \left(\psi \to \phi \right)\right)\to \left(\phi \to \phi \right)$$
3	1 2	ax-mp	$$⊢\phi \to \phi$$