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Theorem ifpbicor 36039
Description: Corollary of commutation of biimplication. (Contributed by RP, 25-Apr-2020.)
Assertion
Ref Expression
ifpbicor  |-  (if- (
ph ,  ps ,  -.  ps )  <-> if- ( ps ,  ph ,  -.  ph ) )

Proof of Theorem ifpbicor
StepHypRef Expression
1 bicom 203 . 2  |-  ( (
ph 
<->  ps )  <->  ( ps  <->  ph ) )
2 ifpdfbi 36037 . 2  |-  ( (
ph 
<->  ps )  <-> if- ( ph ,  ps ,  -.  ps )
)
3 ifpdfbi 36037 . 2  |-  ( ( ps  <->  ph )  <-> if- ( ps ,  ph ,  -.  ph ) )
41, 2, 33bitr3i 278 1  |-  (if- (
ph ,  ps ,  -.  ps )  <-> if- ( ps ,  ph ,  -.  ph ) )
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  df-tru 1440
This theorem is referenced by:  ifpxorcor  36040
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