Theorem bj-sngltagi 37895

Description: The singletonization is included in the tagging. (Contributed by BJ, 6-Oct-2018.)

Assertion

Ref	Expression
bj-sngltagi	⊢ (𝐴 ∈ sngl 𝐵 → 𝐴 ∈ tag 𝐵)

Proof of Theorem bj-sngltagi

Step	Hyp	Ref	Expression
1		bj-snglsstag 37894	. 2 ⊢ sngl 𝐵 ⊆ tag 𝐵
2	1	sseli 3904	1 ⊢ (𝐴 ∈ sngl 𝐵 → 𝐴 ∈ tag 𝐵)

This proof depends on syntax axioms:   → wi 4   ∈ wcel 2144  sngl bj-csngl 37878  tag bj-ctag 37887

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040  ax-8 2146  ax-9 2154  ax-ext 2732

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-tru 1572  df-ex 1812  df-sb 2099  df-clab 2739  df-cleq 2752  df-clel 2835  df-v 3452  df-ss 3896  df-un 4151  df-bj-tag 37888

This theorem is used by:  bj-sngltag  37896  bj-tagci  37897