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Theorem bj-snexg 14904
Description: snexg 4196 from bounded separation. (Contributed by BJ, 5-Oct-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-snexg (𝐴𝑉 → {𝐴} ∈ V)

Proof of Theorem bj-snexg
StepHypRef Expression
1 dfsn2 3618 . 2 {𝐴} = {𝐴, 𝐴}
2 bj-prexg 14903 . . 3 ((𝐴𝑉𝐴𝑉) → {𝐴, 𝐴} ∈ V)
32anidms 397 . 2 (𝐴𝑉 → {𝐴, 𝐴} ∈ V)
41, 3eqeltrid 2274 1 (𝐴𝑉 → {𝐴} ∈ V)
Colors of variables: wff set class
Syntax hints:  wi 4  wcel 2158  Vcvv 2749  {csn 3604  {cpr 3605
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 1457  ax-7 1458  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-8 1514  ax-10 1515  ax-11 1516  ax-i12 1517  ax-bndl 1519  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544  ax-i5r 1545  ax-14 2161  ax-ext 2169  ax-pr 4221  ax-bdor 14808  ax-bdeq 14812  ax-bdsep 14876
This theorem depends on definitions:  df-bi 117  df-tru 1366  df-nf 1471  df-sb 1773  df-clab 2174  df-cleq 2180  df-clel 2183  df-nfc 2318  df-v 2751  df-un 3145  df-sn 3610  df-pr 3611
This theorem is referenced by:  bj-snex  14905  bj-sels  14906  bj-sucexg  14914
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