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Theorem bj-tagss 34731
 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 34726 . 2 tag 𝐴 = (sngl 𝐴 ∪ {∅})
2 bj-snglss 34721 . . 3 sngl 𝐴 ⊆ 𝒫 𝐴
3 0elpw 5228 . . . 4 ∅ ∈ 𝒫 𝐴
4 0ex 5181 . . . . 5 ∅ ∈ V
54snss 4679 . . . 4 (∅ ∈ 𝒫 𝐴 ↔ {∅} ⊆ 𝒫 𝐴)
63, 5mpbi 233 . . 3 {∅} ⊆ 𝒫 𝐴
72, 6unssi 4092 . 2 (sngl 𝐴 ∪ {∅}) ⊆ 𝒫 𝐴
81, 7eqsstri 3928 1 tag 𝐴 ⊆ 𝒫 𝐴
 Colors of variables: wff setvar class Syntax hints:   ∈ wcel 2111   ∪ cun 3858   ⊆ wss 3860  ∅c0 4227  𝒫 cpw 4497  {csn 4525  sngl bj-csngl 34716  tag bj-ctag 34725 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-11 2158  ax-12 2175  ax-ext 2729  ax-sep 5173  ax-nul 5180  ax-pr 5302 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-tru 1541  df-fal 1551  df-ex 1782  df-sb 2070  df-clab 2736  df-cleq 2750  df-clel 2830  df-rex 3076  df-v 3411  df-dif 3863  df-un 3865  df-in 3867  df-ss 3877  df-nul 4228  df-pw 4499  df-sn 4526  df-pr 4528  df-bj-sngl 34717  df-bj-tag 34726 This theorem is referenced by: (None)
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