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Theorem ibibr 332
Description: Implication in terms of implication and biconditional. (Contributed by NM, 29-Apr-2005.) (Proof shortened by Wolf Lammen, 21-Dec-2013.)
Assertion
Ref Expression
ibibr  |-  ( (
ph  ->  ps )  <->  ( ph  ->  ( ps  <->  ph ) ) )

Proof of Theorem ibibr
StepHypRef Expression
1 pm5.501 330 . . 3  |-  ( ph  ->  ( ps  <->  ( ph  <->  ps ) ) )
2 bicom 191 . . 3  |-  ( (
ph 
<->  ps )  <->  ( ps  <->  ph ) )
31, 2syl6bb 252 . 2  |-  ( ph  ->  ( ps  <->  ( ps  <->  ph ) ) )
43pm5.74i 236 1  |-  ( (
ph  ->  ps )  <->  ( ph  ->  ( ps  <->  ph ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176
This theorem is referenced by:  tbt  333  rabxfrd  4571  ufileu  17630  abnotbtaxb  27987
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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