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Theorem ancrd 319
Description: Deduction conjoining antecedent to right of consequent in nested implication. (Contributed by NM, 15-Aug-1994.) (Proof shortened by Wolf Lammen, 1-Nov-2012.)
Hypothesis
Ref Expression
ancrd.1  |-  ( ph  ->  ( ps  ->  ch ) )
Assertion
Ref Expression
ancrd  |-  ( ph  ->  ( ps  ->  ( ch  /\  ps ) ) )

Proof of Theorem ancrd
StepHypRef Expression
1 ancrd.1 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
2 idd 21 . 2  |-  ( ph  ->  ( ps  ->  ps ) )
31, 2jcad 301 1  |-  ( ph  ->  ( ps  ->  ( ch  /\  ps ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia3 106
This theorem is referenced by:  impac  373  euan  2001  reupick  3272  prel12  3600  ssrnres  4841  funmo  4998  funssres  5023  dffo4  5412  dffo5  5413  fzospliti  9518  rexuz3  10340  qredeq  11003  prmdvdsfz  11045
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