Theorem euabex 2763

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 1410	. 2 |- (E!xph -> E*xph)
2		moabex 2762	. 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 957  E!weu 1379  E*wmo 1380  {cab 1462  Vcvv 1808

This theorem is referenced by:  euuni 2877

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 961  ax-gen 962  ax-8 963  ax-10 965  ax-11 966  ax-12 967  ax-13 968  ax-14 969  ax-17 970  ax-4 972  ax-5o 974  ax-6o 977  ax-9o 1122  ax-10o 1139  ax-16 1209  ax-11o 1217  ax-ext 1458  ax-sep 2699  ax-pow 2738

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 980  df-sb 1171  df-eu 1381  df-mo 1382  df-clab 1463  df-cleq 1468  df-clel 1471  df-ne 1585  df-v 1809  df-dif 2046  df-in 2048  df-ss 2050  df-nul 2278  df-pw 2399  df-sn 2409

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