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Theorem ralrimdv 2703
 Description: Inference from Theorem 19.21 of [Margaris] p. 90. (Restricted quantifier version.) (Contributed by NM, 27-May-1998.)
Hypothesis
Ref Expression
ralrimdv.1 (φ → (ψ → (x Aχ)))
Assertion
Ref Expression
ralrimdv (φ → (ψx A χ))
Distinct variable groups:   φ,x   ψ,x
Allowed substitution hints:   χ(x)   A(x)

Proof of Theorem ralrimdv
StepHypRef Expression
1 nfv 1619 . 2 xφ
2 nfv 1619 . 2 xψ
3 ralrimdv.1 . 2 (φ → (ψ → (x Aχ)))
41, 2, 3ralrimd 2702 1 (φ → (ψx A χ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∈ wcel 1710  ∀wral 2614 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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-ex 1542  df-nf 1545  df-ral 2619 This theorem is referenced by:  ralrimdva  2704  ralrimivv  2705  nndisjeq  4429  trrd  5925
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