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Theorem ibibr 344
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 pm5.501 342 . . 3  |-  ( ph  ->  ( ps  <->  ( ph  <->  ps ) ) )
2 bicom 203 . . 3  |-  ( (
ph 
<->  ps )  <->  ( ps  <->  ph ) )
31, 2syl6bb 264 . 2  |-  ( ph  ->  ( ps  <->  ( ps  <->  ph ) ) )
43pm5.74i 248 1  |-  ( (
ph  ->  ps )  <->  ( ph  ->  ( ps  <->  ph ) ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 187
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
This theorem is referenced by:  tbt  345  rabxfrd  4635  ufileu  20911  abnotbtaxb  38124
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