Theorem bj-snglsstag 36957

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 4158	. 2 ⊢ sngl 𝐴 ⊆ (sngl 𝐴 ∪ {∅})
2		df-bj-tag 36951	. 2 ⊢ tag 𝐴 = (sngl 𝐴 ∪ {∅})
3	1, 2	sseqtrri 4013	1 ⊢ sngl 𝐴 ⊆ tag 𝐴

Syntax hints:   ∪ cun 3929   ⊆ wss 3931  ∅c0 4313  {csn 4606  sngl bj-csngl 36941  tag bj-ctag 36950

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-ext 2706

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1542  df-ex 1779  df-sb 2064  df-clab 2713  df-cleq 2726  df-clel 2808  df-v 3465  df-un 3936  df-ss 3948  df-bj-tag 36951

This theorem is referenced by:  bj-sngltagi  36958