Theorem bj-vnex 15871

Description: vnex 4176 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 15869	. 2 |- -. _V e. _V
2		isset 2778	. 2 |- ( _V e. _V <-> E. x x = _V )
3	1, 2	mtbi 672	1 |- -. E. x x = _V

Syntax hints:   -. wn 3   = wceq 1373   E.wex 1515   e. wcel 2176   _Vcvv 2772

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 615  ax-in2 616  ax-5 1470  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-13 2178  ax-14 2179  ax-ext 2187  ax-bdn 15790  ax-bdel 15794  ax-bdsep 15857

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-fal 1379  df-nf 1484  df-sb 1786  df-clab 2192  df-cleq 2198  df-clel 2201  df-v 2774

This theorem is referenced by: (None)