Theorem bj-snex 16853

Description: snex 4317 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 16852	. 2 ⊢ (𝐴 ∈ V → {𝐴} ∈ V)
3	1, 2	ax-mp 5	1 ⊢ {𝐴} ∈ V

Syntax hints:   ∈ wcel 2209  Vcvv 2821  {csn 3705

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 721  ax-5 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-10 1558  ax-11 1559  ax-i12 1560  ax-bndl 1562  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588  ax-14 2212  ax-ext 2220  ax-pr 4341  ax-bdor 16756  ax-bdeq 16760  ax-bdsep 16824

This theorem depends on definitions:  df-bi 117  df-tru 1405  df-nf 1514  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-nfc 2381  df-v 2823  df-un 3224  df-sn 3711  df-pr 3712

This theorem is referenced by:  bj-d0clsepcl  16865