Theorem bj-snglsstag 37004

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 36998	. 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 36988  tag bj-ctag 36997

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2708

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1543  df-ex 1780  df-sb 2066  df-clab 2715  df-cleq 2728  df-clel 2810  df-v 3466  df-un 3936  df-ss 3948  df-bj-tag 36998

This theorem is referenced by:  bj-sngltagi  37005