Theorem bj-sngltagi 37344

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 37343	. 2 ⊢ sngl 𝐵 ⊆ tag 𝐵
2	1	sseli 3911	1 ⊢ (𝐴 ∈ sngl 𝐵 → 𝐴 ∈ tag 𝐵)

Syntax hints:   → wi 4   ∈ wcel 2119  sngl bj-csngl 37327  tag bj-ctag 37336

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-8 2121  ax-9 2129  ax-ext 2711

This theorem depends on definitions:  df-bi 208  df-an 397  df-or 854  df-tru 1550  df-ex 1787  df-sb 2074  df-clab 2718  df-cleq 2731  df-clel 2814  df-v 3433  df-un 3888  df-ss 3900  df-bj-tag 37337

This theorem is referenced by:  bj-sngltag  37345  bj-tagci  37346