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Theorem euabex 4234
Description: The abstraction of a wff with existential uniqueness exists. (Contributed by NM, 25-Nov-1994.)
Assertion
Ref Expression
euabex  |-  ( E! x ph  ->  { x  |  ph }  e.  _V )

Proof of Theorem euabex
StepHypRef Expression
1 eumo 2183 . 2  |-  ( E! x ph  ->  E* x ph )
2 moabex 4232 . 2  |-  ( E* x ph  ->  { x  |  ph }  e.  _V )
31, 2syl 15 1  |-  ( E! x ph  ->  { x  |  ph }  e.  _V )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1684   E!weu 2143   E*wmo 2144   {cab 2269   _Vcvv 2788
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pr 4214
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147  df-mo 2148  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-sn 3646  df-pr 3647
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