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Theorem bicom1 192
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 191 . 2  |-  ( (
ph 
<->  ps )  ->  ( ps  ->  ph ) )
2 bi1 180 . 2  |-  ( (
ph 
<->  ps )  ->  ( ph  ->  ps ) )
31, 2impbid 185 1  |-  ( (
ph 
<->  ps )  ->  ( ps 
<-> 
ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 6    <-> wb 178
This theorem is referenced by:  bicom  193  bicomi  195  wl-bibi1  24087  bisaiaisb  26964
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10
This theorem depends on definitions:  df-bi 179
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