Theorem bj-snex 15343

Description: snex 4214 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 15342	. 2 |- ( A e. _V -> { A } e. _V )
3	1, 2	ax-mp 5	1 |- { A } e. _V

Syntax hints:   e. wcel 2164   _Vcvv 2760   {csn 3618

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 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-14 2167  ax-ext 2175  ax-pr 4238  ax-bdor 15246  ax-bdeq 15250  ax-bdsep 15314

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-nfc 2325  df-v 2762  df-un 3157  df-sn 3624  df-pr 3625

This theorem is referenced by:  bj-d0clsepcl  15355