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

Theorem simplim 168
Description: Simplification. Similar to Theorem *3.26 (Simp) of [WhiteheadRussell] p. 112. (Contributed by NM, 3-Jan-1993.) (Proof shortened by Wolf Lammen, 21-Jul-2012.)
Assertion
Ref Expression
simplim (¬ (𝜑𝜓) → 𝜑)

Proof of Theorem simplim
StepHypRef Expression
1 pm2.21 123 . 2 𝜑 → (𝜑𝜓))
21con1i 149 1 (¬ (𝜑𝜓) → 𝜑)
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:  pm2.5g  169  pm2.521g2  176  impt  179  peirce  203  biimp  216  imbi12  348  pm4.79  998  mptbi12f  34997  ac6s6  35003  rp-fakeimass  39384
  Copyright terms: Public domain W3C validator