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Theorem ralrimd 2702
 Description: Inference from Theorem 19.21 of [Margaris] p. 90. (Restricted quantifier version.) (Contributed by NM, 16-Feb-2004.)
Hypotheses
Ref Expression
ralrimd.1 xφ
ralrimd.2 xψ
ralrimd.3 (φ → (ψ → (x Aχ)))
Assertion
Ref Expression
ralrimd (φ → (ψx A χ))

Proof of Theorem ralrimd
StepHypRef Expression
1 ralrimd.1 . . 3 xφ
2 ralrimd.2 . . 3 xψ
3 ralrimd.3 . . 3 (φ → (ψ → (x Aχ)))
41, 2, 3alrimd 1769 . 2 (φ → (ψx(x Aχ)))
5 df-ral 2619 . 2 (x A χx(x Aχ))
64, 5syl6ibr 218 1 (φ → (ψx A χ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∀wal 1540  Ⅎwnf 1544   ∈ 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:  ralrimdv  2703  ncfinraise  4481
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