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Theorem ancrd 322
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 303 1  |-  ( ph  ->  ( ps  ->  ( ch  /\  ps ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 107
This theorem is referenced by:  impac  376  euan  2031  reupick  3328  prel12  3666  ssrnres  4949  funmo  5106  funssres  5133  dffo4  5534  dffo5  5535  fzospliti  9904  rexuz3  10713  qredeq  11684  prmdvdsfz  11726
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