Theorem elisset 2633

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 2630	. 2 |- ( A e. V -> A e. _V )
2		isset 2625	. 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 1289   E.wex 1426   e. wcel 1438   _Vcvv 2619

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 1381  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-ext 2070

This theorem depends on definitions:  df-bi 115  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-v 2621

This theorem is referenced by:  elex22  2634  elex2  2635  ceqsalt  2645  ceqsalg  2647  cgsexg  2654  cgsex2g  2655  cgsex4g  2656  vtoclgft  2669  vtocleg  2690  vtoclegft  2691  spc2egv  2708  spc2gv  2709  spc3egv  2710  spc3gv  2711  eqvincg  2739  tpid3g  3550  iinexgm  3982  copsex2t  4063  copsex2g  4064  ralxfr2d  4277  rexxfr2d  4278  fliftf  5560  eloprabga  5717  ovmpt4g  5749  spc2ed  5980  eroveu  6363  supelti  6676  genpassl  7062  genpassu  7063  nn1suc  8413  bj-inex  11444