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	⊢ ( 𝜑 → 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		ax-frege1	⊢ ( 𝜑 → ( 𝜓 → 𝜑 ) )
2		frege26	⊢ ( ( 𝜑 → ( 𝜓 → 𝜑 ) ) → ( 𝜑 → 𝜑 ) )
3	1 2	ax-mp	⊢ ( 𝜑 → 𝜑 )