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Theorem bicom1 190
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 189 . 2  |-  ( (
ph 
<->  ps )  ->  ( ps  ->  ph ) )
2 bi1 178 . 2  |-  ( (
ph 
<->  ps )  ->  ( ph  ->  ps ) )
31, 2impbid 183 1  |-  ( (
ph 
<->  ps )  ->  ( ps 
<-> 
ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176
This theorem is referenced by:  bicom  191  bicomi  193  wl-bibi1  24985  bisaiaisb  27985
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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