Theorem euabex 2820

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 1444	. 2 |- (E!xph -> E*xph)
2		moabex 2819	. 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 990  E!weu 1413  E*wmo 1414  {cab 1499  Vcvv 1849

This theorem is referenced by:  euuni 2936

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 994  ax-gen 995  ax-8 996  ax-10 998  ax-11 999  ax-12 1000  ax-13 1001  ax-14 1002  ax-17 1003  ax-4 1005  ax-5o 1007  ax-6o 1010  ax-9o 1155  ax-10o 1173  ax-16 1243  ax-11o 1251  ax-ext 1494  ax-sep 2754  ax-pow 2794

This theorem depends on definitions:  df-bi 145  df-or 222  df-an 223  df-ex 1013  df-sb 1205  df-eu 1415  df-mo 1416  df-clab 1500  df-cleq 1505  df-clel 1508  df-ne 1624  df-v 1850  df-dif 2093  df-in 2095  df-ss 2097  df-nul 2325  df-pw 2447  df-sn 2457

Copyright terms: Public domain