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Theorem bi3 116
Description: Property of the biconditional connective. (Contributed by NM, 11-May-1999.)
Assertion
Ref Expression
bi3  |-  ( (
ph  ->  ps )  -> 
( ( ps  ->  ph )  ->  ( ph  <->  ps ) ) )

Proof of Theorem bi3
StepHypRef Expression
1 df-bi 114 . . 3  |-  ( ( ( ph  <->  ps )  ->  ( ( ph  ->  ps )  /\  ( ps 
->  ph ) ) )  /\  ( ( (
ph  ->  ps )  /\  ( ps  ->  ph )
)  ->  ( ph  <->  ps ) ) )
21simpri 110 . 2  |-  ( ( ( ph  ->  ps )  /\  ( ps  ->  ph ) )  ->  ( ph 
<->  ps ) )
32ex 112 1  |-  ( (
ph  ->  ps )  -> 
( ( ps  ->  ph )  ->  ( ph  <->  ps ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 101    <-> wb 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114
This theorem is referenced by:  impbii  121  impbidd  122  bisym  218
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