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Theorem bicom1 129
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 128 . 2  |-  ( (
ph 
<->  ps )  ->  ( ps  ->  ph ) )
2 bi1 116 . 2  |-  ( (
ph 
<->  ps )  ->  ( ph  ->  ps ) )
31, 2impbid 127 1  |-  ( (
ph 
<->  ps )  ->  ( ps 
<-> 
ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  bicomi  130  bicom  138  pm5.21ndd  654  cbvexdh  1844  elabgf2  10850
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