Users' Mathboxes Mathbox for Richard Penner < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  axfrege52a Structured version   Visualization version   GIF version

Theorem axfrege52a 38467
Description: Justification for ax-frege52a 38468. (Contributed by RP, 17-Apr-2020.)
Assertion
Ref Expression
axfrege52a ((𝜑𝜓) → (if-(𝜑, 𝜃, 𝜒) → if-(𝜓, 𝜃, 𝜒)))

Proof of Theorem axfrege52a
StepHypRef Expression
1 ifpbi1 38139 . 2 ((𝜑𝜓) → (if-(𝜑, 𝜃, 𝜒) ↔ if-(𝜓, 𝜃, 𝜒)))
21biimpd 219 1 ((𝜑𝜓) → (if-(𝜑, 𝜃, 𝜒) → if-(𝜓, 𝜃, 𝜒)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  if-wif 1032
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 197  df-or 384  df-an 385  df-ifp 1033
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator