Theorem bj-snex 16629

Description: snex 4281 from bounded separation. (Contributed by BJ, 5-Oct-2019.) (Proof modification is discouraged.)

Hypothesis

Ref	Expression
bj-snex.1	|- A e. _V

Assertion

Ref	Expression
bj-snex	|- { A } e. _V

Proof of Theorem bj-snex

Step	Hyp	Ref	Expression
1		bj-snex.1	. 2 |- A e. _V
2		bj-snexg 16628	. 2 |- ( A e. _V -> { A } e. _V )
3	1, 2	ax-mp 5	1 |- { A } e. _V

Syntax hints:   e. wcel 2202   _Vcvv 2803   {csn 3673

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-io 717  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-10 1554  ax-11 1555  ax-i12 1556  ax-bndl 1558  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-14 2205  ax-ext 2213  ax-pr 4305  ax-bdor 16532  ax-bdeq 16536  ax-bdsep 16600

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-nf 1510  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2364  df-v 2805  df-un 3205  df-sn 3679  df-pr 3680

This theorem is referenced by:  bj-d0clsepcl  16641