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Theorem anc2r 539
Description: Conjoin antecedent to right of consequent in nested implication. (Contributed by NM, 15-Aug-1994.)
Assertion
Ref Expression
anc2r  |-  ( (
ph  ->  ( ps  ->  ch ) )  ->  ( ph  ->  ( ps  ->  ( ch  /\  ph )
) ) )

Proof of Theorem anc2r
StepHypRef Expression
1 pm3.21 435 . . 3  |-  ( ph  ->  ( ch  ->  ( ch  /\  ph ) ) )
21imim2d 48 . 2  |-  ( ph  ->  ( ( ps  ->  ch )  ->  ( ps  ->  ( ch  /\  ph ) ) ) )
32a2i 12 1  |-  ( (
ph  ->  ( ps  ->  ch ) )  ->  ( ph  ->  ( ps  ->  ( ch  /\  ph )
) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358
This theorem is referenced by:  ssorduni  4593
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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