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Theorem ancl 546
Description: Conjoin antecedent to left of consequent. (Contributed by NM, 15-Aug-1994.)
Assertion
Ref Expression
ancl  |-  ( (
ph  ->  ps )  -> 
( ph  ->  ( ph  /\ 
ps ) ) )

Proof of Theorem ancl
StepHypRef Expression
1 pm3.2 447 . 2  |-  ( ph  ->  ( ps  ->  ( ph  /\  ps ) ) )
21a2i 13 1  |-  ( (
ph  ->  ps )  -> 
( ph  ->  ( ph  /\ 
ps ) ) )
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:  eupickbi  2355  eupickbiOLD  2356  bnj1118  32308  bnj1128  32314  bnj1145  32317  bnj1174  32327
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