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Theorem ancrd 320
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 302 1 (𝜑 → (𝜓 → (𝜒𝜓)))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia3 107
This theorem is referenced by:  impac  374  euan  2005  reupick  3284  prel12  3621  ssrnres  4886  funmo  5043  funssres  5069  dffo4  5461  dffo5  5462  fzospliti  9648  rexuz3  10484  qredeq  11417  prmdvdsfz  11459
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