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Theorem pm3.43i 442
Description: Nested conjunction of antecedents. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
pm3.43i  |-  ( (
ph  ->  ps )  -> 
( ( ph  ->  ch )  ->  ( ph  ->  ( ps  /\  ch ) ) ) )

Proof of Theorem pm3.43i
StepHypRef Expression
1 pm3.2 434 . 2  |-  ( ps 
->  ( ch  ->  ( ps  /\  ch ) ) )
21imim3i 55 1  |-  ( (
ph  ->  ps )  -> 
( ( ph  ->  ch )  ->  ( ph  ->  ( ps  /\  ch ) ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358
This theorem is referenced by:  pm3.43  832  bnj1110  29328
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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