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

Theorem simprim 160
Description: Simplification. Similar to Theorem *3.27 (Simp) of [WhiteheadRussell] p. 112. (Contributed by NM, 3-Jan-1993.) (Proof shortened by Wolf Lammen, 13-Nov-2012.)
Assertion
Ref Expression
simprim (¬ (𝜑 → ¬ 𝜓) → 𝜓)

Proof of Theorem simprim
StepHypRef Expression
1 idd 24 . 2 (𝜑 → (𝜓𝜓))
21impi 158 1 (¬ (𝜑 → ¬ 𝜓) → 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:  impt  167  impbi  196  biimpr  208  imbi12  334
  Copyright terms: Public domain W3C validator