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Theorem ancrd 326
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 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
ancrd (𝜑 → (𝜓 → (𝜒𝜓)))

Proof of Theorem ancrd
StepHypRef Expression
1 ancrd.1 . 2 (𝜑 → (𝜓𝜒))
2 idd 21 . 2 (𝜑 → (𝜓𝜓))
31, 2jcad 307 1 (𝜑 → (𝜓 → (𝜒𝜓)))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108
This theorem is referenced by:  impac  381  euan  2094  reupick  3434  prel12  3786  ssrnres  5089  funmo  5250  funssres  5277  dffo4  5684  dffo5  5685  fzospliti  10205  rexuz3  11030  qredeq  12127  prmdvdsfz  12170
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