Users' Mathboxes Mathbox for Richard Penner < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  ax-frege1 Structured version   Visualization version   GIF version

Axiom ax-frege1 37001
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  37003  rp-frege3g  37005  frege3  37006  frege5  37011  rp-6frege  37014  frege26  37021  frege27  37022  frege11  37025  frege24  37026  frege36  37050
  Copyright terms: Public domain W3C validator