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Theorem reurex 2523
 Description: Restricted unique existence implies restricted existence. (Contributed by NM, 19-Aug-1999.)
Assertion
Ref Expression
reurex (∃!𝑥𝐴 𝜑 → ∃𝑥𝐴 𝜑)

Proof of Theorem reurex
StepHypRef Expression
1 reu5 2522 . 2 (∃!𝑥𝐴 𝜑 ↔ (∃𝑥𝐴 𝜑 ∧ ∃*𝑥𝐴 𝜑))
21simplbi 259 1 (∃!𝑥𝐴 𝜑 → ∃𝑥𝐴 𝜑)
 Colors of variables: wff set class Syntax hints:   → wi 4  ∃wrex 2307  ∃!wreu 2308  ∃*wrmo 2309 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-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-eu 1903  df-mo 1904  df-rex 2312  df-reu 2313  df-rmo 2314 This theorem is referenced by:  reu3  2731  prsrriota  6872  elrealeu  6906
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