Users' Mathboxes Mathbox for Richard Penner < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  ax-frege28 Structured version   Visualization version   GIF version

Axiom ax-frege28 41406
Description: Contraposition. Identical to con3 153. Theorem *2.16 of [WhiteheadRussell] p. 103. Axiom 28 of [Frege1879] p. 43. (Contributed by RP, 24-Dec-2019.) (New usage is discouraged.)
Assertion
Ref Expression
ax-frege28 ((𝜑𝜓) → (¬ 𝜓 → ¬ 𝜑))

Detailed syntax breakdown of Axiom ax-frege28
StepHypRef Expression
1 wph . 2 wff 𝜑
2 wps . 2 wff 𝜓
32wn 3 . . 3 wff ¬ 𝜓
41wn 3 . . 3 wff ¬ 𝜑
53, 4wi 4 . 2 wff 𝜓 → ¬ 𝜑)
61, 2, 5bj-0 34716 1 wff ((𝜑𝜓) → (¬ 𝜓 → ¬ 𝜑))
Colors of variables: wff setvar class
This axiom is referenced by:  frege29  41407  frege33  41412  frege54cor0a  41439
  Copyright terms: Public domain W3C validator