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Theorem ancrd 537
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 519 1 (φ → (ψ → (χ ψ)))
Colors of variables: wff setvar class
Syntax hints:  wi 4   wa 358
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 177  df-an 360
This theorem is referenced by:  impac  604  euan  2261  2eu1  2284  reupick  3539  spfininduct  4540  vinf  4555  ssrnres  5059  funssres  5144  dffo4  5423  dffo5  5424
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