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| Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-tagn0 | Structured version Visualization version GIF version | ||
| Description: The tagging of a class is nonempty. (Contributed by BJ, 6-Apr-2019.) | 
| Ref | Expression | 
|---|---|
| bj-tagn0 | ⊢ tag 𝐴 ≠ ∅ | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | bj-0eltag 36980 | . 2 ⊢ ∅ ∈ tag 𝐴 | |
| 2 | 1 | ne0ii 4343 | 1 ⊢ tag 𝐴 ≠ ∅ | 
| Colors of variables: wff setvar class | 
| Syntax hints: ≠ wne 2939 ∅c0 4332 tag bj-ctag 36976 | 
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1794 ax-4 1808 ax-5 1909 ax-6 1966 ax-7 2006 ax-8 2109 ax-9 2117 ax-ext 2707 ax-nul 5305 | 
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 848 df-tru 1542 df-fal 1552 df-ex 1779 df-sb 2064 df-clab 2714 df-cleq 2728 df-clel 2815 df-ne 2940 df-v 3481 df-dif 3953 df-un 3955 df-nul 4333 df-sn 4626 df-bj-tag 36977 | 
| This theorem is referenced by: bj-1upln0 37011 bj-2upln1upl 37026 | 
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