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Theorem rexlimdv3a 2435
 Description: Inference from Theorem 19.23 of [Margaris] p. 90 (restricted quantifier version). Frequently-used variant of rexlimdv 2432. (Contributed by NM, 7-Jun-2015.)
Hypothesis
Ref Expression
rexlimdv3a.1 ((𝜑𝑥𝐴𝜓) → 𝜒)
Assertion
Ref Expression
rexlimdv3a (𝜑 → (∃𝑥𝐴 𝜓𝜒))
Distinct variable groups:   𝜑,𝑥   𝜒,𝑥
Allowed substitution hints:   𝜓(𝑥)   𝐴(𝑥)

Proof of Theorem rexlimdv3a
StepHypRef Expression
1 rexlimdv3a.1 . . 3 ((𝜑𝑥𝐴𝜓) → 𝜒)
213exp 1103 . 2 (𝜑 → (𝑥𝐴 → (𝜓𝜒)))
32rexlimdv 2432 1 (𝜑 → (∃𝑥𝐴 𝜓𝜒))
 Colors of variables: wff set class Syntax hints:   → wi 4   ∧ w3a 885   ∈ wcel 1393  ∃wrex 2307 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-17 1419  ax-ial 1427  ax-i5r 1428 This theorem depends on definitions:  df-bi 110  df-3an 887  df-nf 1350  df-ral 2311  df-rex 2312 This theorem is referenced by:  resqrtcl  9627
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