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Theorem oibabs 879
Description: Absorption of disjunction into equivalence. (Contributed by NM, 6-Aug-1995.) (Proof shortened by Wolf Lammen, 3-Nov-2013.)
Assertion
Ref Expression
oibabs  |-  ( ( ( ph  \/  ps )  ->  ( ph  <->  ps )
)  <->  ( ph  <->  ps )
)

Proof of Theorem oibabs
StepHypRef Expression
1 norbi 857 . . 3  |-  ( -.  ( ph  \/  ps )  ->  ( ph  <->  ps )
)
2 id 22 . . 3  |-  ( (
ph 
<->  ps )  ->  ( ph 
<->  ps ) )
31, 2ja 161 . 2  |-  ( ( ( ph  \/  ps )  ->  ( ph  <->  ps )
)  ->  ( ph  <->  ps ) )
4 ax-1 6 . 2  |-  ( (
ph 
<->  ps )  ->  (
( ph  \/  ps )  ->  ( ph  <->  ps )
) )
53, 4impbii 188 1  |-  ( ( ( ph  \/  ps )  ->  ( ph  <->  ps )
)  <->  ( ph  <->  ps )
)
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 184    \/ wo 368
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 185  df-or 370
This theorem is referenced by: (None)
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