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Theorem ifpnorcor 36038
Description: Corollary of commutation of nor. (Contributed by RP, 25-Apr-2020.)
Assertion
Ref Expression
ifpnorcor  |-  (if- (
ph ,  -.  ph ,  -.  ps )  <-> if- ( ps ,  -.  ps ,  -.  ph ) )

Proof of Theorem ifpnorcor
StepHypRef Expression
1 ifporcor 36019 . . 3  |-  (if- (
ph ,  ph ,  ps )  <-> if- ( ps ,  ps ,  ph ) )
21notbii 297 . 2  |-  ( -. if- ( ph ,  ph ,  ps )  <->  -. if- ( ps ,  ps ,  ph ) )
3 ifpnot23 36036 . 2  |-  ( -. if- ( ph ,  ph ,  ps )  <-> if- ( ph ,  -.  ph ,  -.  ps ) )
4 ifpnot23 36036 . 2  |-  ( -. if- ( ps ,  ps ,  ph )  <-> if- ( ps ,  -.  ps ,  -.  ph ) )
52, 3, 43bitr3i 278 1  |-  (if- (
ph ,  -.  ph ,  -.  ps )  <-> if- ( ps ,  -.  ps ,  -.  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
This theorem is referenced by: (None)
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