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Theorem bj-tagss 36981
Description: The tagging of a class is included in its powerclass. (Contributed by BJ, 6-Oct-2018.)
Assertion
Ref Expression
bj-tagss tag 𝐴 ⊆ 𝒫 𝐴

Proof of Theorem bj-tagss
StepHypRef Expression
1 df-bj-tag 36976 . 2 tag 𝐴 = (sngl 𝐴 ∪ {∅})
2 bj-snglss 36971 . . 3 sngl 𝐴 ⊆ 𝒫 𝐴
3 0elpw 5356 . . . 4 ∅ ∈ 𝒫 𝐴
4 0ex 5307 . . . . 5 ∅ ∈ V
54snss 4785 . . . 4 (∅ ∈ 𝒫 𝐴 ↔ {∅} ⊆ 𝒫 𝐴)
63, 5mpbi 230 . . 3 {∅} ⊆ 𝒫 𝐴
72, 6unssi 4191 . 2 (sngl 𝐴 ∪ {∅}) ⊆ 𝒫 𝐴
81, 7eqsstri 4030 1 tag 𝐴 ⊆ 𝒫 𝐴
Colors of variables: wff setvar class
Syntax hints:  wcel 2108  cun 3949  wss 3951  c0 4333  𝒫 cpw 4600  {csn 4626  sngl bj-csngl 36966  tag bj-ctag 36975
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-11 2157  ax-12 2177  ax-ext 2708  ax-sep 5296  ax-nul 5306  ax-pr 5432
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-rex 3071  df-v 3482  df-dif 3954  df-un 3956  df-ss 3968  df-nul 4334  df-pw 4602  df-sn 4627  df-pr 4629  df-bj-sngl 36967  df-bj-tag 36976
This theorem is referenced by: (None)
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