ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  anbi2ci GIF version

Theorem anbi2ci 454
Description: Variant of anbi2i 452 with commutation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (Proof shortened by Andrew Salmon, 14-Jun-2011.)
Hypothesis
Ref Expression
bi.aa (𝜑𝜓)
Assertion
Ref Expression
anbi2ci ((𝜑𝜒) ↔ (𝜒𝜓))

Proof of Theorem anbi2ci
StepHypRef Expression
1 bi.aa . . 3 (𝜑𝜓)
21anbi1i 453 . 2 ((𝜑𝜒) ↔ (𝜓𝜒))
3 ancom 264 . 2 ((𝜓𝜒) ↔ (𝜒𝜓))
42, 3bitri 183 1 ((𝜑𝜒) ↔ (𝜒𝜓))
Colors of variables: wff set class
Syntax hints:  wa 103  wb 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  clabel  2266  ordpwsucss  4482  asymref  4924  supmoti  6880  xmeter  12619
  Copyright terms: Public domain W3C validator