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Theorem ibib 331
Description: Implication in terms of implication and biconditional. (Contributed by NM, 31-Mar-1994.) (Proof shortened by Wolf Lammen, 24-Jan-2013.)
Assertion
Ref Expression
ibib  |-  ( (
ph  ->  ps )  <->  ( ph  ->  ( ph  <->  ps )
) )

Proof of Theorem ibib
StepHypRef Expression
1 pm5.501 330 . 2  |-  ( ph  ->  ( ps  <->  ( ph  <->  ps ) ) )
21pm5.74i 236 1  |-  ( (
ph  ->  ps )  <->  ( ph  ->  ( ph  <->  ps )
) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176
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 177
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