Users' Mathboxes Mathbox for Richard Penner < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  ifpancor Structured version   Visualization version   GIF version

Theorem ifpancor 41810
Description: Corollary of commutation of and. (Contributed by RP, 25-Apr-2020.)
Assertion
Ref Expression
ifpancor (if-(𝜑, 𝜓, 𝜑) ↔ if-(𝜓, 𝜑, 𝜓))

Proof of Theorem ifpancor
StepHypRef Expression
1 ancom 462 . 2 ((𝜑𝜓) ↔ (𝜓𝜑))
2 ifpdfan2 41809 . 2 ((𝜑𝜓) ↔ if-(𝜑, 𝜓, 𝜑))
3 ifpdfan2 41809 . 2 ((𝜓𝜑) ↔ if-(𝜓, 𝜑, 𝜓))
41, 2, 33bitr3i 301 1 (if-(𝜑, 𝜓, 𝜑) ↔ if-(𝜓, 𝜑, 𝜓))
Colors of variables: wff setvar class
Syntax hints:  wb 205  wa 397  if-wif 1062
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 206  df-an 398  df-or 847  df-ifp 1063
This theorem is referenced by:  ifpnancor  41827
  Copyright terms: Public domain W3C validator