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

Theorem anbi2ci 432
Description: Variant of anbi2i 430 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 ((φ χ) ↔ (χ ψ))

Proof of Theorem anbi2ci
StepHypRef Expression
1 bi.aa . . 3 (φψ)
21anbi1i 431 . 2 ((φ χ) ↔ (ψ χ))
3 ancom 253 . 2 ((ψ χ) ↔ (χ ψ))
42, 3bitri 173 1 ((φ χ) ↔ (χ ψ))
Colors of variables: wff set class
Syntax hints:   wa 97  wb 98
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  clabel  2160  ordpwsucss  4243  asymref  4653
  Copyright terms: Public domain W3C validator