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Theorem bj-snglsstag 32162
 Description: The singletonization is included in the tagging. (Contributed by BJ, 6-Oct-2018.)
Assertion
Ref Expression
bj-snglsstag sngl 𝐴 ⊆ tag 𝐴

Proof of Theorem bj-snglsstag
StepHypRef Expression
1 ssun1 3738 . 2 sngl 𝐴 ⊆ (sngl 𝐴 ∪ {∅})
2 df-bj-tag 32156 . 2 tag 𝐴 = (sngl 𝐴 ∪ {∅})
31, 2sseqtr4i 3601 1 sngl 𝐴 ⊆ tag 𝐴
 Colors of variables: wff setvar class Syntax hints:   ∪ cun 3538   ⊆ wss 3540  ∅c0 3874  {csn 4125  sngl bj-csngl 32146  tag bj-ctag 32155 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-v 3175  df-un 3545  df-in 3547  df-ss 3554  df-bj-tag 32156 This theorem is referenced by:  bj-sngltagi  32163
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