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Theorem aibandbiaiffaiffb 27838
Description: A closed form showing (a implies b and b implies a) same-as (a same-as b) (Contributed by Jarvin Udandy, 3-Sep-2016.)
Assertion
Ref Expression
aibandbiaiffaiffb  |-  ( ( ( ph  ->  ps )  /\  ( ps  ->  ph ) )  <->  ( ph  <->  ps ) )

Proof of Theorem aibandbiaiffaiffb
StepHypRef Expression
1 dfbi2 610 . 2  |-  ( (
ph 
<->  ps )  <->  ( ( ph  ->  ps )  /\  ( ps  ->  ph )
) )
21bicomi 194 1  |-  ( ( ( ph  ->  ps )  /\  ( ps  ->  ph ) )  <->  ( ph  <->  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 177    /\ wa 359
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 178  df-an 361
  Copyright terms: Public domain W3C validator