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Theorem 4exmidOLD 998
Description: Obsolete proof of 4exmid 997 as of 29-Oct-2021. (Contributed by David Abernethy, 28-Jan-2014.) (New usage is discouraged.) (Proof modification is discouraged.)
Assertion
Ref Expression
4exmidOLD  |-  ( ( ( ph  /\  ps )  \/  ( -.  ph 
/\  -.  ps )
)  \/  ( (
ph  /\  -.  ps )  \/  ( ps  /\  -.  ph ) ) )

Proof of Theorem 4exmidOLD
StepHypRef Expression
1 exmid 431 . 2  |-  ( (
ph 
<->  ps )  \/  -.  ( ph  <->  ps ) )
2 dfbi3 994 . . 3  |-  ( (
ph 
<->  ps )  <->  ( ( ph  /\  ps )  \/  ( -.  ph  /\  -.  ps ) ) )
3 xor 935 . . 3  |-  ( -.  ( ph  <->  ps )  <->  ( ( ph  /\  -.  ps )  \/  ( ps  /\  -.  ph )
) )
42, 3orbi12i 543 . 2  |-  ( ( ( ph  <->  ps )  \/  -.  ( ph  <->  ps )
)  <->  ( ( (
ph  /\  ps )  \/  ( -.  ph  /\  -.  ps ) )  \/  ( ( ph  /\  -.  ps )  \/  ( ps  /\  -.  ph )
) ) )
51, 4mpbi 220 1  |-  ( ( ( ph  /\  ps )  \/  ( -.  ph 
/\  -.  ps )
)  \/  ( (
ph  /\  -.  ps )  \/  ( ps  /\  -.  ph ) ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    <-> wb 196    \/ wo 383    /\ wa 384
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 197  df-or 385  df-an 386
This theorem is referenced by: (None)
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