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

Theorem bianir 1074
Description: A closed form of mpbir 222, analogous to pm2.27 42 (assertion). (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (Proof shortened by Roger Witte, 17-Aug-2020.)
Assertion
Ref Expression
bianir ((𝜑 ∧ (𝜓𝜑)) → 𝜓)

Proof of Theorem bianir
StepHypRef Expression
1 biimpr 211 . 2 ((𝜓𝜑) → (𝜑𝜓))
21impcom 396 1 ((𝜑 ∧ (𝜓𝜑)) → 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 197  wa 384
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 198  df-an 385
This theorem is referenced by:  suppimacnv  7536  lgsqrmodndvds  25291  bnj970  31338  bnj1001  31349  bj-bibibi  32884
  Copyright terms: Public domain W3C validator