Theorem bj-tagci 36952

Description: Characterization of the elements of 𝐵 in terms of elements of its tagged version. (Contributed by BJ, 6-Oct-2018.)

Assertion

Ref	Expression
bj-tagci	⊢ (𝐴 ∈ 𝐵 → {𝐴} ∈ tag 𝐵)

Proof of Theorem bj-tagci

Step	Hyp	Ref	Expression
1		bj-snglc 36937	. 2 ⊢ (𝐴 ∈ 𝐵 ↔ {𝐴} ∈ sngl 𝐵)
2		bj-sngltagi 36950	. 2 ⊢ ({𝐴} ∈ sngl 𝐵 → {𝐴} ∈ tag 𝐵)
3	1, 2	sylbi 217	1 ⊢ (𝐴 ∈ 𝐵 → {𝐴} ∈ tag 𝐵)

Syntax hints:   → wi 4   ∈ wcel 2108  {csn 4648  sngl bj-csngl 36933  tag bj-ctag 36942

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-11 2158  ax-12 2178  ax-ext 2711  ax-sep 5317  ax-pr 5447

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 847  df-tru 1540  df-ex 1778  df-sb 2065  df-clab 2718  df-cleq 2732  df-clel 2819  df-rex 3077  df-v 3490  df-un 3981  df-ss 3993  df-sn 4649  df-pr 4651  df-bj-sngl 36934  df-bj-tag 36943

This theorem is referenced by: (None)