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Theorem reximdva 2726
 Description: Deduction quantifying both antecedent and consequent, based on Theorem 19.22 of [Margaris] p. 90. (Contributed by NM, 22-May-1999.)
Hypothesis
Ref Expression
reximdva.1 ((φ x A) → (ψχ))
Assertion
Ref Expression
reximdva (φ → (x A ψx A χ))
Distinct variable group:   φ,x
Allowed substitution hints:   ψ(x)   χ(x)   A(x)

Proof of Theorem reximdva
StepHypRef Expression
1 reximdva.1 . . 3 ((φ x A) → (ψχ))
21ex 423 . 2 (φ → (x A → (ψχ)))
32reximdvai 2724 1 (φ → (x A ψx A χ))
 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-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:  sfindbl  4530  dffo4  5423  weds  5938  nenpw1pwlem2  6085  nchoicelem19  6307
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