Theorem bj-vnex 16171

Description: vnex 4194 from bounded separation. (Contributed by BJ, 18-Nov-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
bj-vnex	|- -. E. x x = _V

Proof of Theorem bj-vnex

Step	Hyp	Ref	Expression
1		bj-vprc 16169	. 2 |- -. _V e. _V
2		isset 2786	. 2 |- ( _V e. _V <-> E. x x = _V )
3	1, 2	mtbi 674	1 |- -. E. x x = _V

Syntax hints:   -. wn 3   = wceq 1375   E.wex 1518   e. wcel 2180   _Vcvv 2779

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-in1 617  ax-in2 618  ax-5 1473  ax-gen 1475  ax-ie1 1519  ax-ie2 1520  ax-8 1530  ax-4 1536  ax-17 1552  ax-i9 1556  ax-ial 1560  ax-13 2182  ax-14 2183  ax-ext 2191  ax-bdn 16090  ax-bdel 16094  ax-bdsep 16157

This theorem depends on definitions:  df-bi 117  df-tru 1378  df-fal 1381  df-nf 1487  df-sb 1789  df-clab 2196  df-cleq 2202  df-clel 2205  df-v 2781

This theorem is referenced by: (None)