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Theorem bicom1 199
Description: Commutative law for equivalence. (Contributed by Wolf Lammen, 10-Nov-2012.)
Assertion
Ref Expression
bicom1  |-  ( (
ph 
<->  ps )  ->  ( ps 
<-> 
ph ) )

Proof of Theorem bicom1
StepHypRef Expression
1 bi2 198 . 2  |-  ( (
ph 
<->  ps )  ->  ( ps  ->  ph ) )
2 bi1 186 . 2  |-  ( (
ph 
<->  ps )  ->  ( ph  ->  ps ) )
31, 2impbid 191 1  |-  ( (
ph 
<->  ps )  ->  ( ps 
<-> 
ph ) )
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:  bicom  200  bicomi  202  bisaiaisb  31533  bj-con3ALT  33119  bj-frege55lem2a  36753
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