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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-tagci | Structured version Visualization version GIF version |
Description: Characterization of the elements of 𝐵 in terms of elements of its tagged version. (Contributed by BJ, 6-Oct-2018.) |
Ref | Expression |
---|---|
bj-tagci | ⊢ (𝐴 ∈ 𝐵 → {𝐴} ∈ tag 𝐵) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-snglc 35718 | . 2 ⊢ (𝐴 ∈ 𝐵 ↔ {𝐴} ∈ sngl 𝐵) | |
2 | bj-sngltagi 35731 | . 2 ⊢ ({𝐴} ∈ sngl 𝐵 → {𝐴} ∈ tag 𝐵) | |
3 | 1, 2 | sylbi 216 | 1 ⊢ (𝐴 ∈ 𝐵 → {𝐴} ∈ tag 𝐵) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∈ wcel 2106 {csn 4623 sngl bj-csngl 35714 tag bj-ctag 35723 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1913 ax-6 1971 ax-7 2011 ax-8 2108 ax-9 2116 ax-11 2154 ax-12 2171 ax-ext 2703 ax-sep 5293 ax-pr 5421 |
This theorem depends on definitions: df-bi 206 df-an 397 df-or 846 df-tru 1544 df-ex 1782 df-sb 2068 df-clab 2710 df-cleq 2724 df-clel 2810 df-rex 3071 df-v 3476 df-un 3950 df-in 3952 df-ss 3962 df-sn 4624 df-pr 4626 df-bj-sngl 35715 df-bj-tag 35724 |
This theorem is referenced by: (None) |
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