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Theorem anc2l 538
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 pm5.42 531 . 2  |-  ( (
ph  ->  ( ps  ->  ch ) )  <->  ( ph  ->  ( ps  ->  ( ph  /\  ch ) ) ) )
21biimpi 186 1  |-  ( (
ph  ->  ( ps  ->  ch ) )  ->  ( ph  ->  ( ps  ->  (
ph  /\  ch )
) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360
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