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Theorem bicom1 130
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 129 . 2  |-  ( (
ph 
<->  ps )  ->  ( ps  ->  ph ) )
2 bi1 117 . 2  |-  ( (
ph 
<->  ps )  ->  ( ph  ->  ps ) )
31, 2impbid 128 1  |-  ( (
ph 
<->  ps )  ->  ( ps 
<-> 
ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  bicomi  131  bicom  139  pm5.21ndd  694  cbvexdh  1898  elabgf2  13017
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