Theorem bj-sngltagi 37646

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 37645	. 2 ⊢ sngl 𝐵 ⊆ tag 𝐵
2	1	sseli 3932	1 ⊢ (𝐴 ∈ sngl 𝐵 → 𝐴 ∈ tag 𝐵)

This proof depends on syntax axioms:   → wi 4   ∈ wcel 2142  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-sngltag  37647  bj-tagci  37648