Metamath Proof Explorer


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