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Theorem ifpxorcor 36090
Description: Corollary of commutation of biimplication. (Contributed by RP, 25-Apr-2020.)
Assertion
Ref Expression
ifpxorcor  |-  (if- (
ph ,  -.  ps ,  ps )  <-> if- ( ps ,  -.  ph ,  ph ) )

Proof of Theorem ifpxorcor
StepHypRef Expression
1 ifpbicor 36089 . 2  |-  (if- (
ph ,  -.  ps ,  -.  -.  ps )  <-> if- ( -.  ps ,  ph ,  -.  ph ) )
2 notnot 292 . . 3  |-  ( ps  <->  -. 
-.  ps )
3 ifpbi3 36081 . . 3  |-  ( ( ps  <->  -.  -.  ps )  ->  (if- ( ph ,  -.  ps ,  ps )  <-> if- (
ph ,  -.  ps ,  -.  -.  ps )
) )
42, 3ax-mp 5 . 2  |-  (if- (
ph ,  -.  ps ,  ps )  <-> if- ( ph ,  -.  ps ,  -.  -.  ps ) )
5 ifpn 1430 . 2  |-  (if- ( ps ,  -.  ph ,  ph )  <-> if- ( -.  ps ,  ph ,  -.  ph ) )
61, 4, 53bitr4i 280 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: (None)
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