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Theorem anc2ri 558
Description: Deduction conjoining antecedent to right of consequent in nested implication. (Contributed by NM, 15-Aug-1994.) (Proof shortened by Wolf Lammen, 7-Dec-2012.)
Hypothesis
Ref Expression
anc2ri.1  |-  ( ph  ->  ( ps  ->  ch ) )
Assertion
Ref Expression
anc2ri  |-  ( ph  ->  ( ps  ->  ( ch  /\  ph ) ) )

Proof of Theorem anc2ri
StepHypRef Expression
1 anc2ri.1 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
2 id 22 . 2  |-  ( ph  ->  ph )
31, 2jctird 544 1  |-  ( ph  ->  ( ps  ->  ( ch  /\  ph ) ) )
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:  equvini  2060  fv3  5878  bropopvvv  6863  issiga  27767  ontopbas  29486  bj-gl4lem  33274
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