Theorem bj-snex 15526

Description: snex 4218 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 15525	. 2 |- ( A e. _V -> { A } e. _V )
3	1, 2	ax-mp 5	1 |- { A } e. _V

Syntax hints:   e. wcel 2167   _Vcvv 2763   {csn 3622

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 1461  ax-7 1462  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-8 1518  ax-10 1519  ax-11 1520  ax-i12 1521  ax-bndl 1523  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548  ax-i5r 1549  ax-14 2170  ax-ext 2178  ax-pr 4242  ax-bdor 15429  ax-bdeq 15433  ax-bdsep 15497

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1475  df-sb 1777  df-clab 2183  df-cleq 2189  df-clel 2192  df-nfc 2328  df-v 2765  df-un 3161  df-sn 3628  df-pr 3629

This theorem is referenced by:  bj-d0clsepcl  15538