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Theorem impor 30109
Description: An equivalent formula for implying a disjunction. (Contributed by Giovanni Mascellani, 15-Sep-2017.)
Assertion
Ref Expression
impor  |-  ( (
ph  ->  ( ps  \/  ch ) )  <->  ( ( -.  ph  \/  ps )  \/  ch ) )

Proof of Theorem impor
StepHypRef Expression
1 imor 412 . 2  |-  ( (
ph  ->  ( ps  \/  ch ) )  <->  ( -.  ph  \/  ( ps  \/  ch ) ) )
2 orass 524 . . . 4  |-  ( ( ( -.  ph  \/  ps )  \/  ch ) 
<->  ( -.  ph  \/  ( ps  \/  ch ) ) )
32bicomi 202 . . 3  |-  ( ( -.  ph  \/  ( ps  \/  ch ) )  <-> 
( ( -.  ph  \/  ps )  \/  ch ) )
43bibi2i 313 . 2  |-  ( ( ( ph  ->  ( ps  \/  ch ) )  <-> 
( -.  ph  \/  ( ps  \/  ch ) ) )  <->  ( ( ph  ->  ( ps  \/  ch ) )  <->  ( ( -.  ph  \/  ps )  \/  ch ) ) )
51, 4mpbi 208 1  |-  ( (
ph  ->  ( ps  \/  ch ) )  <->  ( ( -.  ph  \/  ps )  \/  ch ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> 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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