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Theorem anclb 547
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 504 . 2  |-  ( ph  ->  ( ps  <->  ( ph  /\ 
ps ) ) )
21pm5.74i 245 1  |-  ( (
ph  ->  ps )  <->  ( ph  ->  ( ph  /\  ps ) ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 184    /\ wa 369
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 185  df-an 371
This theorem is referenced by:  pm4.71  630  difin  3687  bnj1021  32259  dihglblem6  35293
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