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Theorem ifpnot23d 36043
Description: Negation of conditional logical operator. (Contributed by RP, 25-Apr-2020.)
Assertion
Ref Expression
ifpnot23d  |-  ( -. if- ( ph ,  -.  ps ,  -.  ch )  <-> if- (
ph ,  ps ,  ch ) )

Proof of Theorem ifpnot23d
StepHypRef Expression
1 ifpnot23 36036 . 2  |-  ( -. if- ( ph ,  -.  ps ,  -.  ch )  <-> if- (
ph ,  -.  -.  ps ,  -.  -.  ch ) )
2 notnot 292 . . 3  |-  ( ps  <->  -. 
-.  ps )
3 notnot 292 . . 3  |-  ( ch  <->  -. 
-.  ch )
4 ifpbi23 36030 . . 3  |-  ( ( ( ps  <->  -.  -.  ps )  /\  ( ch  <->  -.  -.  ch ) )  ->  (if- ( ph ,  ps ,  ch )  <-> if- ( ph ,  -.  -.  ps ,  -.  -.  ch ) ) )
52, 3, 4mp2an 676 . 2  |-  (if- (
ph ,  ps ,  ch )  <-> if- ( ph ,  -.  -.  ps ,  -.  -.  ch ) )
61, 5bitr4i 255 1  |-  ( -. if- ( ph ,  -.  ps ,  -.  ch )  <-> if- (
ph ,  ps ,  ch ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    <-> wb 187  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:  ifpororb  36063
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