Theorem bj-snex 16511

Description: snex 4275 from bounded separation. (Contributed by BJ, 5-Oct-2019.) (Proof modification is discouraged.)

Hypothesis

Ref	Expression
bj-snex.1	⊢ 𝐴 ∈ V

Assertion

Ref	Expression
bj-snex	⊢ {𝐴} ∈ V

Proof of Theorem bj-snex

Step	Hyp	Ref	Expression
1		bj-snex.1	. 2 ⊢ 𝐴 ∈ V
2		bj-snexg 16510	. 2 ⊢ (𝐴 ∈ V → {𝐴} ∈ V)
3	1, 2	ax-mp 5	1 ⊢ {𝐴} ∈ V

Syntax hints:   ∈ wcel 2202  Vcvv 2802  {csn 3669

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 716  ax-5 1495  ax-7 1496  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-10 1553  ax-11 1554  ax-i12 1555  ax-bndl 1557  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582  ax-i5r 1583  ax-14 2205  ax-ext 2213  ax-pr 4299  ax-bdor 16414  ax-bdeq 16418  ax-bdsep 16482

This theorem depends on definitions:  df-bi 117  df-tru 1400  df-nf 1509  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2363  df-v 2804  df-un 3204  df-sn 3675  df-pr 3676

This theorem is referenced by:  bj-d0clsepcl  16523