Theorem bj-snglsstag 37645

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 4130	. 2 ⊢ sngl 𝐴 ⊆ (sngl 𝐴 ∪ {∅})
2		df-bj-tag 37639	. 2 ⊢ tag 𝐴 = (sngl 𝐴 ∪ {∅})
3	1, 2	sseqtrri 3985	1 ⊢ sngl 𝐴 ⊆ tag 𝐴

This proof depends on syntax axioms:   ∪ cun 3902   ⊆ wss 3904  ∅c0 4285  {csn 4588  sngl bj-csngl 37629  tag bj-ctag 37638

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1824  ax-4 1838  ax-5 1939  ax-6 1996  ax-7 2037  ax-8 2144  ax-9 2152  ax-ext 2734

This proof depends on definitions:  df-bi 210  df-an 401  df-or 861  df-tru 1572  df-ex 1809  df-sb 2096  df-clab 2741  df-cleq 2754  df-clel 2837  df-v 3456  df-un 3909  df-ss 3921  df-bj-tag 37639

This theorem is used by:  bj-sngltagi  37646