Theorem bj-snex 14516

Description: snex 4184 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 14515	. 2 |- ( A e. _V -> { A } e. _V )
3	1, 2	ax-mp 5	1 |- { A } e. _V

Syntax hints:   e. wcel 2148   _Vcvv 2737   {csn 3592

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 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-14 2151  ax-ext 2159  ax-pr 4208  ax-bdor 14419  ax-bdeq 14423  ax-bdsep 14487

This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-v 2739  df-un 3133  df-sn 3598  df-pr 3599

This theorem is referenced by:  bj-d0clsepcl  14528