MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  conax1 Structured version   Visualization version   GIF version

Theorem conax1 173
Description: Contrapositive of ax-1 6. (Contributed by BJ, 28-Oct-2023.)
Assertion
Ref Expression
conax1 (¬ (𝜑𝜓) → ¬ 𝜓)

Proof of Theorem conax1
StepHypRef Expression
1 ax-1 6 . 2 (𝜓 → (𝜑𝜓))
21con3i 157 1 (¬ (𝜑𝜓) → ¬ 𝜓)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem is referenced by:  conax1k  174  pm2.521g  177  rp-fakeimass  40217
  Copyright terms: Public domain W3C validator