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Theorem bisym 281
Description: Express symmetries of theorems in terms of biconditionals. (Contributed by Wolf Lammen, 14-May-2013.)
Assertion
Ref Expression
bisym  |-  ( ( ( ph  ->  ps )  ->  ( ch  ->  th ) )  ->  (
( ( ps  ->  ph )  ->  ( th  ->  ch ) )  -> 
( ( ph  <->  ps )  ->  ( ch  <->  th )
) ) )

Proof of Theorem bisym
StepHypRef Expression
1 bi3 179 . 2  |-  ( ( ch  ->  th )  ->  ( ( th  ->  ch )  ->  ( ch  <->  th ) ) )
21bi3ant 280 1  |-  ( ( ( ph  ->  ps )  ->  ( ch  ->  th ) )  ->  (
( ( ps  ->  ph )  ->  ( th  ->  ch ) )  -> 
( ( ph  <->  ps )  ->  ( ch  <->  th )
) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176
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 177
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