Theorem elisset 2791

Description: An element of a class exists. (Contributed by NM, 1-May-1995.)

Assertion

Ref	Expression
elisset	|- ( A e. V -> E. x x = A )

Distinct variable group:   x, A

Allowed substitution hint:   V( x)

Proof of Theorem elisset

Step	Hyp	Ref	Expression
1		elex 2788	. 2 |- ( A e. V -> A e. _V )
2		isset 2783	. 2 |- ( A e. _V <-> E. x x = A )
3	1, 2	sylib 122	1 |- ( A e. V -> E. x x = A )

Syntax hints:   -> wi 4   = wceq 1373   E.wex 1516   e. wcel 2178   _Vcvv 2776

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1471  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-ext 2189

This theorem depends on definitions:  df-bi 117  df-sb 1787  df-clab 2194  df-cleq 2200  df-clel 2203  df-v 2778

This theorem is referenced by:  elex22  2792  elex2  2793  ceqsalt  2803  ceqsalg  2805  cgsexg  2812  cgsex2g  2813  cgsex4g  2814  vtoclgft  2828  vtocleg  2851  vtoclegft  2852  spc2egv  2870  spc2gv  2871  spc3egv  2872  spc3gv  2873  eqvincg  2904  tpid3g  3758  iinexgm  4214  copsex2t  4307  copsex2g  4308  ralxfr2d  4529  rexxfr2d  4530  fliftf  5891  eloprabga  6055  ovmpt4g  6091  spc2ed  6342  eroveu  6736  supelti  7130  genpassl  7672  genpassu  7673  eqord1  8591  nn1suc  9090  bj-inex  16042