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Theorem ancrb 535
Description: Conjoin antecedent to right of consequent. (Contributed by NM, 25-Jul-1999.) (Proof shortened by Wolf Lammen, 24-Mar-2013.)
Assertion
Ref Expression
ancrb  |-  ( (
ph  ->  ps )  <->  ( ph  ->  ( ps  /\  ph ) ) )

Proof of Theorem ancrb
StepHypRef Expression
1 iba 491 . 2  |-  ( ph  ->  ( ps  <->  ( ps  /\ 
ph ) ) )
21pm5.74i 238 1  |-  ( (
ph  ->  ps )  <->  ( ph  ->  ( ps  /\  ph ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 178    /\ wa 360
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 179  df-an 362
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