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Theorem euabex 5376
Description: The abstraction of a wff with existential uniqueness exists. (Contributed by NM, 25-Nov-1994.)
Assertion
Ref Expression
euabex (∃!𝑥𝜑 → {𝑥𝜑} ∈ V)

Proof of Theorem euabex
StepHypRef Expression
1 eumo 2578 . 2 (∃!𝑥𝜑 → ∃*𝑥𝜑)
2 moabex 5374 . 2 (∃*𝑥𝜑 → {𝑥𝜑} ∈ V)
31, 2syl 17 1 (∃!𝑥𝜑 → {𝑥𝜑} ∈ V)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2106  ∃*wmo 2538  ∃!weu 2568  {cab 2715  Vcvv 3431
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-10 2137  ax-11 2154  ax-12 2171  ax-ext 2709  ax-sep 5223  ax-nul 5230  ax-pr 5352
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-tru 1542  df-fal 1552  df-ex 1783  df-nf 1787  df-sb 2068  df-mo 2540  df-eu 2569  df-clab 2716  df-cleq 2730  df-clel 2816  df-nfc 2889  df-rab 3073  df-v 3433  df-dif 3891  df-un 3893  df-in 3895  df-ss 3905  df-nul 4259  df-sn 4564  df-pr 4566
This theorem is referenced by:  sprval  44888  prprval  44923
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