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Theorem rb-bijust 1520
Description: Justification for rb-imdf 1521. (Contributed by Anthony Hart, 17-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
rb-bijust  |-  ( (
ph 
<->  ps )  <->  -.  ( -.  ( -.  ph  \/  ps )  \/  -.  ( -.  ps  \/  ph ) ) )

Proof of Theorem rb-bijust
StepHypRef Expression
1 dfbi1 185 . 2  |-  ( (
ph 
<->  ps )  <->  -.  (
( ph  ->  ps )  ->  -.  ( ps  ->  ph ) ) )
2 imor 402 . . . 4  |-  ( (
ph  ->  ps )  <->  ( -.  ph  \/  ps ) )
3 imor 402 . . . . 5  |-  ( ( ps  ->  ph )  <->  ( -.  ps  \/  ph ) )
43notbii 288 . . . 4  |-  ( -.  ( ps  ->  ph )  <->  -.  ( -.  ps  \/  ph ) )
52, 4imbi12i 317 . . 3  |-  ( ( ( ph  ->  ps )  ->  -.  ( ps  ->  ph ) )  <->  ( ( -.  ph  \/  ps )  ->  -.  ( -.  ps  \/  ph ) ) )
65notbii 288 . 2  |-  ( -.  ( ( ph  ->  ps )  ->  -.  ( ps  ->  ph ) )  <->  -.  (
( -.  ph  \/  ps )  ->  -.  ( -.  ps  \/  ph )
) )
7 pm4.62 409 . . 3  |-  ( ( ( -.  ph  \/  ps )  ->  -.  ( -.  ps  \/  ph )
)  <->  ( -.  ( -.  ph  \/  ps )  \/  -.  ( -.  ps  \/  ph ) ) )
87notbii 288 . 2  |-  ( -.  ( ( -.  ph  \/  ps )  ->  -.  ( -.  ps  \/  ph ) )  <->  -.  ( -.  ( -.  ph  \/  ps )  \/  -.  ( -.  ps  \/  ph ) ) )
91, 6, 83bitri 263 1  |-  ( (
ph 
<->  ps )  <->  -.  ( -.  ( -.  ph  \/  ps )  \/  -.  ( -.  ps  \/  ph ) ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 177    \/ wo 358
This theorem is referenced by:  rb-imdf  1521
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 178  df-or 360
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