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Theorem frege27 40345
Description: We cannot (at the same time) affirm 𝜑 and deny 𝜑. Identical to id 22. Proposition 27 of [Frege1879] p. 43. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege27 (𝜑𝜑)

Proof of Theorem frege27
StepHypRef Expression
1 ax-frege1 40324 . 2 (𝜑 → (𝜓𝜑))
2 frege26 40344 . 2 ((𝜑 → (𝜓𝜑)) → (𝜑𝜑))
31, 2ax-mp 5 1 (𝜑𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-frege1 40324  ax-frege8 40343
This theorem is referenced by:  frege42  40380
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