Users' Mathboxes Mathbox for Richard Penner < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  ifpdfor2 Structured version   Unicode version

Theorem ifpdfor2 35803
Description: Define or in terms of conditional logic operator. (Contributed by RP, 20-Apr-2020.)
Assertion
Ref Expression
ifpdfor2  |-  ( (
ph  \/  ps )  <-> if- (
ph ,  ph ,  ps ) )

Proof of Theorem ifpdfor2
StepHypRef Expression
1 pm2.1 418 . . 3  |-  ( -. 
ph  \/  ph )
21biantrur 508 . 2  |-  ( (
ph  \/  ps )  <->  ( ( -.  ph  \/  ph )  /\  ( ph  \/  ps ) ) )
3 dfifp4 1424 . 2  |-  (if- (
ph ,  ph ,  ps )  <->  ( ( -. 
ph  \/  ph )  /\  ( ph  \/  ps )
) )
42, 3bitr4i 255 1  |-  ( (
ph  \/  ps )  <-> if- (
ph ,  ph ,  ps ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    <-> wb 187    \/ wo 369    /\ wa 370  if-wif 1420
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 188  df-or 371  df-an 372  df-ifp 1421
This theorem is referenced by:  ifporcor  35804
  Copyright terms: Public domain W3C validator