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Theorem aibandbiaiaiffb 38195
Description: A closed form showing (a implies b and b implies a) implies (a same-as b) (Contributed by Jarvin Udandy, 3-Sep-2016.)
Assertion
Ref Expression
aibandbiaiaiffb  |-  ( ( ( ph  ->  ps )  /\  ( ps  ->  ph ) )  ->  ( ph 
<->  ps ) )

Proof of Theorem aibandbiaiaiffb
StepHypRef Expression
1 dfbi2 632 . 2  |-  ( (
ph 
<->  ps )  <->  ( ( ph  ->  ps )  /\  ( ps  ->  ph )
) )
21biimpri 209 1  |-  ( ( ( ph  ->  ps )  /\  ( ps  ->  ph ) )  ->  ( ph 
<->  ps ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 187    /\ wa 370
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 188  df-an 372
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator