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Axiom ax-frege1 40339
Description: The case in which 𝜑 is denied, 𝜓 is affirmed, and 𝜑 is affirmed is excluded. This is evident since 𝜑 cannot at the same time be denied and affirmed. Axiom 1 of [Frege1879] p. 26. Identical to ax-1 6. (Contributed by RP, 24-Dec-2019.) (New usage is discouraged.)
Assertion
Ref Expression
ax-frege1 (𝜑 → (𝜓𝜑))

Detailed syntax breakdown of Axiom ax-frege1
StepHypRef Expression
1 wph . 2 wff 𝜑
2 wps . . 3 wff 𝜓
32, 1wi 4 . 2 wff (𝜓𝜑)
41, 3wi 4 1 wff (𝜑 → (𝜓𝜑))
Colors of variables: wff setvar class
This axiom is referenced by:  rp-simp2-frege  40341  rp-frege3g  40343  frege3  40344  frege5  40349  rp-6frege  40352  frege26  40359  frege27  40360  frege11  40363  frege24  40364  frege36  40388
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