Users' Mathboxes Mathbox for Richard Penner < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  ifpnot23c Structured version   Visualization version   Unicode version
Theorem ifpnot23c 37829
Description: Negation of conditional logical operator. (Contributed by RP, 25-Apr-2020.)
Assertion
Ref Expression
ifpnot23c |- ( -. if- ( ph , ps , -. ch ) <-> if- ( ph , -. ps , ch ) )
Proof of Theorem ifpnot23c
StepHypRef Expression
1 ifpnot23 37823 . 2 |- ( -. if- ( ph , ps , -. ch ) <-> if- ( ph , -. ps , -. -. ch ) )
2 notnotb 304 . . 3 |- ( ch <-> -. -. ch )
3 ifpbi3 37812 . . 3 |- ( ( ch <-> -. -. ch ) -> (if- ( ph , -. ps , ch ) <-> if- ( ph , -. ps , -. -. ch ) ) )
42, 3ax-mp 5 . 2 |- (if- ( ph , -. ps , ch ) <-> if- ( ph , -. ps , -. -. ch ) )
51, 4bitr4i 267 1 |- ( -. if- ( ph , ps , -. ch ) <-> if- ( ph , -. ps , ch ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3   <-> wb 196  if-wif 1012
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 385  df-an 386  df-ifp 1013
This theorem is referenced by:  ifpnim1  37842  ifpnim2  37844
  Copyright terms: Public domain W3C validator