Theorem elisset 2828

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 2825	. 2 |- ( A e. V -> A e. _V )
2		isset 2820	. 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 1398   E.wex 1541   e. wcel 2203   _Vcvv 2813

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 1496  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-ext 2214

This theorem depends on definitions:  df-bi 117  df-sb 1812  df-clab 2219  df-cleq 2225  df-clel 2228  df-v 2815

This theorem is referenced by:  elex22  2829  elex2  2830  ceqsalt  2840  ceqsalg  2842  cgsexg  2849  cgsex2g  2850  cgsex4g  2851  vtoclgft  2865  vtocleg  2888  vtoclegft  2889  spc2egv  2907  spc2gv  2908  spc3egv  2909  spc3gv  2910  eqvincg  2941  tpid3g  3807  iinexgm  4266  copsex2t  4361  copsex2g  4362  ralxfr2d  4585  rexxfr2d  4586  fliftf  5972  eloprabga  6140  ovmpt4g  6176  spc2ed  6429  eroveu  6860  supelti  7293  genpassl  7839  genpassu  7840  eqord1  8757  nn1suc  9256  bj-inex  16677