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Theorem anclb 532
Description: Conjoin antecedent to left of consequent. Theorem *4.7 of [WhiteheadRussell] p. 120. (Contributed by NM, 25-Jul-1999.) (Proof shortened by Wolf Lammen, 24-Mar-2013.)
Assertion
Ref Expression
anclb  |-  ( (
ph  ->  ps )  <->  ( ph  ->  ( ph  /\  ps ) ) )

Proof of Theorem anclb
StepHypRef Expression
1 ibar 492 . 2  |-  ( ph  ->  ( ps  <->  ( ph  /\ 
ps ) ) )
21pm5.74i 238 1  |-  ( (
ph  ->  ps )  <->  ( ph  ->  ( ph  /\  ps ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 6    <-> wb 178    /\ wa 360
This theorem is referenced by:  pm4.71  614  difin  3367  bnj1021  28029  dihglblem6  30681
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10
This theorem depends on definitions:  df-bi 179  df-an 362
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