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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 34290 | . 2 ⊢ ∅ ∈ tag 𝐴 | |
2 | 1 | ne0ii 4302 | 1 ⊢ tag 𝐴 ≠ ∅ |
Colors of variables: wff setvar class |
Syntax hints: ≠ wne 3016 ∅c0 4290 tag bj-ctag 34286 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1907 ax-6 1966 ax-7 2011 ax-8 2112 ax-9 2120 ax-10 2141 ax-11 2157 ax-12 2173 ax-ext 2793 ax-nul 5209 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-tru 1536 df-ex 1777 df-nf 1781 df-sb 2066 df-clab 2800 df-cleq 2814 df-clel 2893 df-nfc 2963 df-ne 3017 df-v 3496 df-dif 3938 df-un 3940 df-nul 4291 df-sn 4567 df-bj-tag 34287 |
This theorem is referenced by: bj-1upln0 34321 bj-2upln1upl 34336 |
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