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Theorem anc2l 555
Description: Conjoin antecedent to left of consequent in nested implication. (Contributed by NM, 10-Aug-1994.) (Proof shortened by Wolf Lammen, 14-Jul-2013.)
Assertion
Ref Expression
anc2l  |-  ( (
ph  ->  ( ps  ->  ch ) )  ->  ( ph  ->  ( ps  ->  (
ph  /\  ch )
) ) )

Proof of Theorem anc2l
StepHypRef Expression
1 pm5.42 548 . 2  |-  ( (
ph  ->  ( ps  ->  ch ) )  <->  ( ph  ->  ( ps  ->  ( ph  /\  ch ) ) ) )
21biimpi 194 1  |-  ( (
ph  ->  ( ps  ->  ch ) )  ->  ( ph  ->  ( ps  ->  (
ph  /\  ch )
) ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ 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: (None)
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