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Theorem rexlimdvaa 2739
 Description: Inference from Theorem 19.23 of [Margaris] p. 90 (restricted quantifier version). (Contributed by Mario Carneiro, 15-Jun-2016.)
Hypothesis
Ref Expression
rexlimdvaa.1 ((φ (x A ψ)) → χ)
Assertion
Ref Expression
rexlimdvaa (φ → (x A ψχ))
Distinct variable groups:   φ,x   χ,x
Allowed substitution hints:   ψ(x)   A(x)

Proof of Theorem rexlimdvaa
StepHypRef Expression
1 rexlimdvaa.1 . . 3 ((φ (x A ψ)) → χ)
21expr 598 . 2 ((φ x A) → (ψχ))
32rexlimdva 2738 1 (φ → (x A ψχ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 358   ∈ wcel 1710  ∃wrex 2615 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-6 1729  ax-11 1746 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-nf 1545  df-ral 2619  df-rex 2620 This theorem is referenced by:  rexlimddv  2742
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