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Theorem ralrimdva 2704
 Description: Inference from Theorem 19.21 of [Margaris] p. 90. (Restricted quantifier version.) (Contributed by NM, 2-Feb-2008.)
Hypothesis
Ref Expression
ralrimdva.1 ((φ x A) → (ψχ))
Assertion
Ref Expression
ralrimdva (φ → (ψx A χ))
Distinct variable groups:   φ,x   ψ,x
Allowed substitution hints:   χ(x)   A(x)

Proof of Theorem ralrimdva
StepHypRef Expression
1 ralrimdva.1 . . . 4 ((φ x A) → (ψχ))
21ex 423 . . 3 (φ → (x A → (ψχ)))
32com23 72 . 2 (φ → (ψ → (x Aχ)))
43ralrimdv 2703 1 (φ → (ψx A χ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 358   ∈ wcel 1710  ∀wral 2614 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-nf 1545  df-ral 2619 This theorem is referenced by: (None)
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