Theorem euabex 2757

Description: The abstraction of a wff with existential uniqueness exists.

Assertion

Ref	Expression
euabex	|- (E!xph -> {x | ph} e. V)

Proof of Theorem euabex

Step	Hyp	Ref	Expression
1		eumo 1404	. 2 |- (E!xph -> E*xph)
2		moabex 2756	. 2 |- (E*xph -> {x | ph} e. V)
3	1, 2	syl 10	1 |- (E!xph -> {x | ph} e. V)

Syntax hints:   -> wi 3   e. wcel 955  E!weu 1373  E*wmo 1374  {cab 1456  Vcvv 1802

This theorem is referenced by:  euuni 2871

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 959  ax-gen 960  ax-8 961  ax-10 963  ax-11 964  ax-12 965  ax-13 966  ax-14 967  ax-17 968  ax-4 970  ax-5o 972  ax-6o 975  ax-9o 1119  ax-10o 1136  ax-16 1206  ax-11o 1213  ax-ext 1452  ax-sep 2693  ax-pow 2732

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 978  df-sb 1168  df-eu 1375  df-mo 1376  df-clab 1457  df-cleq 1462  df-clel 1465  df-ne 1579  df-v 1803  df-dif 2039  df-in 2041  df-ss 2043  df-nul 2271  df-pw 2392  df-sn 2402

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