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Theorem ancrd 309
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 → (χ ψ)))

Proof of Theorem ancrd
StepHypRef Expression
1 ancrd.1 . 2 (φ → (ψχ))
2 idd 21 . 2 (φ → (ψψ))
31, 2jcad 291 1 (φ → (ψ → (χ ψ)))
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia3 101
This theorem is referenced by:  impac  363  euan  1953  reupick  3215  prel12  3533  ssrnres  4706  funmo  4860  funssres  4885  dffo4  5258  dffo5  5259  fzospliti  8762
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