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Theorem bj-bisym 33661
Description: This used to be in the main part. (Contributed by Wolf Lammen, 14-May-2013.) (Revised by BJ, 14-Jun-2019.)
Assertion
Ref Expression
bj-bisym  |-  ( ( ( ph  ->  ps )  ->  ( ch  ->  th ) )  ->  (
( ( ps  ->  ph )  ->  ( th  ->  ch ) )  -> 
( ( ph  <->  ps )  ->  ( ch  <->  th )
) ) )

Proof of Theorem bj-bisym
StepHypRef Expression
1 bi3 187 . 2  |-  ( ( ch  ->  th )  ->  ( ( th  ->  ch )  ->  ( ch  <->  th ) ) )
21bj-bi3ant 33660 1  |-  ( ( ( ph  ->  ps )  ->  ( ch  ->  th ) )  ->  (
( ( ps  ->  ph )  ->  ( th  ->  ch ) )  -> 
( ( ph  <->  ps )  ->  ( ch  <->  th )
) ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 184
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
This theorem is referenced by: (None)
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