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Theorem ancr 532
Description: Conjoin antecedent to right of consequent. (Contributed by NM, 15-Aug-1994.)
Assertion
Ref Expression
ancr  |-  ( (
ph  ->  ps )  -> 
( ph  ->  ( ps 
/\  ph ) ) )

Proof of Theorem ancr
StepHypRef Expression
1 pm3.21 435 . 2  |-  ( ph  ->  ( ps  ->  ( ps  /\  ph ) ) )
21a2i 12 1  |-  ( (
ph  ->  ps )  -> 
( ph  ->  ( ps 
/\  ph ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358
This theorem is referenced by:  bimsc1  904  reupick2  3454  intmin4  3891  lukshef-ax2  24854  pm14.122b  27623  bnj1098  28815
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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