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Theorem rexlimiva 2428
 Description: Inference from Theorem 19.23 of [Margaris] p. 90 (restricted quantifier version). (Contributed by NM, 18-Dec-2006.)
Hypothesis
Ref Expression
rexlimiva.1 ((𝑥𝐴𝜑) → 𝜓)
Assertion
Ref Expression
rexlimiva (∃𝑥𝐴 𝜑𝜓)
Distinct variable group:   𝜓,𝑥
Allowed substitution hints:   𝜑(𝑥)   𝐴(𝑥)

Proof of Theorem rexlimiva
StepHypRef Expression
1 rexlimiva.1 . . 3 ((𝑥𝐴𝜑) → 𝜓)
21ex 108 . 2 (𝑥𝐴 → (𝜑𝜓))
32rexlimiv 2427 1 (∃𝑥𝐴 𝜑𝜓)
 Colors of variables: wff set class Syntax hints:   → wi 4   ∧ wa 97   ∈ 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-nf 1350  df-ral 2311  df-rex 2312 This theorem is referenced by:  unon  4237  reg2exmidlema  4259  ssfiexmid  6336  diffitest  6344  finnum  6363  dmaddpqlem  6475  nqpi  6476  nq0nn  6540  recexprlemm  6722  rexanuz  9587  r19.2uz  9591  bj-nn0suc  10089  bj-nn0sucALT  10103
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