Theorem elisset 2614

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 2611	. 2 |- ( A e. V -> A e. _V )
2		isset 2606	. 2 |- ( A e. _V <-> E. x x = A )
3	1, 2	sylib 120	1 |- ( A e. V -> E. x x = A )

Syntax hints:   -> wi 4   = wceq 1285   E.wex 1422   e. wcel 1434   _Vcvv 2602

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-ext 2064

This theorem depends on definitions:  df-bi 115  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-v 2604

This theorem is referenced by:  elex22  2615  elex2  2616  ceqsalt  2626  ceqsalg  2628  cgsexg  2635  cgsex2g  2636  cgsex4g  2637  vtoclgft  2650  vtocleg  2670  vtoclegft  2671  spc2egv  2688  spc2gv  2689  spc3egv  2690  spc3gv  2691  eqvincg  2720  tpid3g  3513  iinexgm  3937  copsex2t  4008  copsex2g  4009  ralxfr2d  4222  rexxfr2d  4223  fliftf  5470  eloprabga  5622  ovmpt4g  5654  spc2ed  5885  eroveu  6263  supelti  6474  genpassl  6776  genpassu  6777  nn1suc  8125  bj-inex  10856