MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  pm2.61 Structured version   Visualization version   GIF version

Theorem pm2.61 183
Description: Theorem *2.61 of [WhiteheadRussell] p. 107. Useful for eliminating an antecedent. (Contributed by NM, 4-Jan-1993.) (Proof shortened by Wolf Lammen, 22-Sep-2013.)
Assertion
Ref Expression
pm2.61 ((𝜑𝜓) → ((¬ 𝜑𝜓) → 𝜓))

Proof of Theorem pm2.61
StepHypRef Expression
1 pm2.6 182 . 2 ((¬ 𝜑𝜓) → ((𝜑𝜓) → 𝜓))
21com12 32 1 ((𝜑𝜓) → ((¬ 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:  bnj1109  30562  isltrn2N  34883  ltrnid  34898  ltrneq  34912  onfrALT  38243  onfrALTVD  38607
  Copyright terms: Public domain W3C validator