Theorem bj-snglsstag 37726

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 4124	. 2 ⊢ sngl 𝐴 ⊆ (sngl 𝐴 ∪ {∅})
2		df-bj-tag 37720	. 2 ⊢ tag 𝐴 = (sngl 𝐴 ∪ {∅})
3	1, 2	sseqtrri 3980	1 ⊢ sngl 𝐴 ⊆ tag 𝐴

This proof depends on syntax axioms:   ∪ cun 3897   ⊆ wss 3899  ∅c0 4279  {csn 4584  sngl bj-csngl 37710  tag bj-ctag 37719

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-8 2147  ax-9 2155  ax-ext 2732

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-tru 1573  df-ex 1813  df-sb 2100  df-clab 2739  df-cleq 2752  df-clel 2835  df-v 3452  df-un 3904  df-ss 3916  df-bj-tag 37720

This theorem is used by:  bj-sngltagi  37727