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Theorem reximdvai 2491
 Description: Deduction quantifying both antecedent and consequent, based on Theorem 19.22 of [Margaris] p. 90. (Contributed by NM, 14-Nov-2002.)
Hypothesis
Ref Expression
reximdvai.1 (𝜑 → (𝑥𝐴 → (𝜓𝜒)))
Assertion
Ref Expression
reximdvai (𝜑 → (∃𝑥𝐴 𝜓 → ∃𝑥𝐴 𝜒))
Distinct variable group:   𝜑,𝑥
Allowed substitution hints:   𝜓(𝑥)   𝜒(𝑥)   𝐴(𝑥)

Proof of Theorem reximdvai
StepHypRef Expression
1 nfv 1476 . 2 𝑥𝜑
2 reximdvai.1 . 2 (𝜑 → (𝑥𝐴 → (𝜓𝜒)))
31, 2reximdai 2489 1 (𝜑 → (∃𝑥𝐴 𝜓 → ∃𝑥𝐴 𝜒))
 Colors of variables: wff set class Syntax hints:   → wi 4   ∈ wcel 1448  ∃wrex 2376 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1391  ax-gen 1393  ax-ie1 1437  ax-ie2 1438  ax-4 1455  ax-17 1474  ax-ial 1482 This theorem depends on definitions:  df-bi 116  df-nf 1405  df-ral 2380  df-rex 2381 This theorem is referenced by:  reximdv  2492  reximdva  2493  reuind  2842
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