Theorem bj-sngltagi 37566

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 37565	. 2 ⊢ sngl 𝐵 ⊆ tag 𝐵
2	1	sseli 3941	1 ⊢ (𝐴 ∈ sngl 𝐵 → 𝐴 ∈ tag 𝐵)

Syntax hints:   → wi 4   ∈ wcel 2150  sngl bj-csngl 37549  tag bj-ctag 37558

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1823  ax-4 1837  ax-5 1938  ax-6 1995  ax-7 2036  ax-8 2152  ax-9 2160  ax-ext 2742

This theorem depends on definitions:  df-bi 210  df-an 401  df-or 861  df-tru 1571  df-ex 1808  df-sb 2099  df-clab 2749  df-cleq 2762  df-clel 2845  df-v 3464  df-un 3918  df-ss 3930  df-bj-tag 37559

This theorem is referenced by:  bj-sngltag  37567  bj-tagci  37568