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Theorem ifpnotnotb 36037
Description: Factor conditional logic operator over negation in terms 2 and 3. (Contributed by RP, 21-Apr-2020.)
Assertion
Ref Expression
ifpnotnotb  |-  (if- (
ph ,  -.  ps ,  -.  ch )  <->  -. if- ( ph ,  ps ,  ch )
)

Proof of Theorem ifpnotnotb
StepHypRef Expression
1 ifpnot23 36036 . 2  |-  ( -. if- ( ph ,  ps ,  ch )  <-> if- ( ph ,  -.  ps ,  -.  ch ) )
21bicomi 205 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:  ifpananb  36064  ifpnannanb  36065  ifpxorxorb  36069
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