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Theorem ancrd 313
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 295 1 (𝜑 → (𝜓 → (𝜒𝜓)))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia3 105
This theorem is referenced by:  impac  367  euan  1972  reupick  3249  prel12  3570  ssrnres  4791  funmo  4945  funssres  4970  dffo4  5343  dffo5  5344  fzospliti  9134  rexuz3  9817
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