Theorem bj-sngltagi 35099

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 35098	. 2 ⊢ sngl 𝐵 ⊆ tag 𝐵
2	1	sseli 3913	1 ⊢ (𝐴 ∈ sngl 𝐵 → 𝐴 ∈ tag 𝐵)

Syntax hints:   → wi 4   ∈ wcel 2108  sngl bj-csngl 35082  tag bj-ctag 35091

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2110  ax-9 2118  ax-ext 2709

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 844  df-tru 1542  df-ex 1784  df-sb 2069  df-clab 2716  df-cleq 2730  df-clel 2817  df-v 3424  df-un 3888  df-in 3890  df-ss 3900  df-bj-tag 35092

This theorem is referenced by:  bj-sngltag  35100  bj-tagci  35101