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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 33808 | . 2 ⊢ ∅ ∈ tag 𝐴 | |
2 | 1 | ne0ii 4191 | 1 ⊢ tag 𝐴 ≠ ∅ |
Colors of variables: wff setvar class |
Syntax hints: ≠ wne 2967 ∅c0 4180 tag bj-ctag 33804 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1758 ax-4 1772 ax-5 1869 ax-6 1928 ax-7 1965 ax-8 2052 ax-9 2059 ax-10 2079 ax-11 2093 ax-12 2106 ax-ext 2750 ax-nul 5068 |
This theorem depends on definitions: df-bi 199 df-an 388 df-or 834 df-tru 1510 df-ex 1743 df-nf 1747 df-sb 2016 df-clab 2759 df-cleq 2771 df-clel 2846 df-nfc 2918 df-ne 2968 df-v 3417 df-dif 3834 df-un 3836 df-nul 4181 df-sn 4443 df-bj-tag 33805 |
This theorem is referenced by: bj-1upln0 33839 bj-2upln1upl 33854 |
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