Theorem frege27 44810

Description: We cannot (at the same time) affirm 𝜑 and deny 𝜑. Identical to id 23. Proposition 27 of [Frege1879] p. 43. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
frege27	⊢ (𝜑 → 𝜑)

Proof of Theorem frege27

Step	Hyp	Ref	Expression
1		ax-frege1 44789	. 2 ⊢ (𝜑 → (𝜓 → 𝜑))
2		frege26 44809	. 2 ⊢ ((𝜑 → (𝜓 → 𝜑)) → (𝜑 → 𝜑))
3	1, 2	ax-mp 5	1 ⊢ (𝜑 → 𝜑)

This proof depends on syntax axioms:   → wi 4

This proof depends on axioms:  ax-mp 5  ax-frege1 44789  ax-frege8 44808

This theorem is used by:  frege42  44845