Theorem bj-tagci 36945

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 36930	. 2 ⊢ (𝐴 ∈ 𝐵 ↔ {𝐴} ∈ sngl 𝐵)
2		bj-sngltagi 36943	. 2 ⊢ ({𝐴} ∈ sngl 𝐵 → {𝐴} ∈ tag 𝐵)
3	1, 2	sylbi 217	1 ⊢ (𝐴 ∈ 𝐵 → {𝐴} ∈ tag 𝐵)

Syntax hints:   → wi 4   ∈ wcel 2109  {csn 4585  sngl bj-csngl 36926  tag bj-ctag 36935

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-11 2158  ax-12 2178  ax-ext 2701  ax-sep 5246  ax-pr 5382

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1543  df-ex 1780  df-sb 2066  df-clab 2708  df-cleq 2721  df-clel 2803  df-rex 3054  df-v 3446  df-un 3916  df-ss 3928  df-sn 4586  df-pr 4588  df-bj-sngl 36927  df-bj-tag 36936

This theorem is referenced by: (None)