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Theorem biorfi 398
Description: A wff is equivalent to its disjunction with falsehood. (Contributed by NM, 23-Mar-1995.)
Hypothesis
Ref Expression
biorfi.1  |-  -.  ph
Assertion
Ref Expression
biorfi  |-  ( ps  <->  ( ps  \/  ph )
)

Proof of Theorem biorfi
StepHypRef Expression
1 biorfi.1 . 2  |-  -.  ph
2 orc 376 . . 3  |-  ( ps 
->  ( ps  \/  ph ) )
3 orel2 374 . . 3  |-  ( -. 
ph  ->  ( ( ps  \/  ph )  ->  ps ) )
42, 3impbid2 197 . 2  |-  ( -. 
ph  ->  ( ps  <->  ( ps  \/  ph ) ) )
51, 4ax-mp 8 1  |-  ( ps  <->  ( ps  \/  ph )
)
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 178    \/ wo 359
This theorem is referenced by:  pm4.43  895  dn1  934  indifdir  3599  un0  3654  opthprc  4927  imadif  5530  xrsupss  10889  mdegleb  19989  ind1a  24420
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 179  df-or 361
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