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Theorem bj-tagss 36587
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 36582 . 2 tag 𝐴 = (sngl 𝐴 ∪ {∅})
2 bj-snglss 36577 . . 3 sngl 𝐴 ⊆ 𝒫 𝐴
3 0elpw 5356 . . . 4 ∅ ∈ 𝒫 𝐴
4 0ex 5308 . . . . 5 ∅ ∈ V
54snss 4791 . . . 4 (∅ ∈ 𝒫 𝐴 ↔ {∅} ⊆ 𝒫 𝐴)
63, 5mpbi 229 . . 3 {∅} ⊆ 𝒫 𝐴
72, 6unssi 4183 . 2 (sngl 𝐴 ∪ {∅}) ⊆ 𝒫 𝐴
81, 7eqsstri 4011 1 tag 𝐴 ⊆ 𝒫 𝐴
Colors of variables: wff setvar class
Syntax hints:  wcel 2098  cun 3942  wss 3944  c0 4322  𝒫 cpw 4604  {csn 4630  sngl bj-csngl 36572  tag bj-ctag 36581
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-11 2146  ax-12 2166  ax-ext 2696  ax-sep 5300  ax-nul 5307  ax-pr 5429
This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2703  df-cleq 2717  df-clel 2802  df-rex 3060  df-v 3463  df-dif 3947  df-un 3949  df-ss 3961  df-nul 4323  df-pw 4606  df-sn 4631  df-pr 4633  df-bj-sngl 36573  df-bj-tag 36582
This theorem is referenced by: (None)
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