Theorem bj-snglsstag 37467

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

Step	Hyp	Ref	Expression
1		ssun1 4131	. 2 ⊢ sngl 𝐴 ⊆ (sngl 𝐴 ∪ {∅})
2		df-bj-tag 37461	. 2 ⊢ tag 𝐴 = (sngl 𝐴 ∪ {∅})
3	1, 2	sseqtrri 3986	1 ⊢ sngl 𝐴 ⊆ tag 𝐴

Syntax hints:   ∪ cun 3903   ⊆ wss 3905  ∅c0 4286  {csn 4583  sngl bj-csngl 37451  tag bj-ctag 37460

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1816  ax-4 1830  ax-5 1931  ax-6 1988  ax-7 2029  ax-8 2145  ax-9 2153  ax-ext 2735

This theorem depends on definitions:  df-bi 209  df-an 400  df-or 859  df-tru 1564  df-ex 1801  df-sb 2092  df-clab 2742  df-cleq 2755  df-clel 2838  df-v 3457  df-un 3910  df-ss 3922  df-bj-tag 37461

This theorem is referenced by:  bj-sngltagi  37468