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Mirrors > Home > MPE Home > Th. List > nel0 | Structured version Visualization version Unicode version |
Description: From the general negation of membership in , infer that is the empty set. (Contributed by BJ, 6-Oct-2018.) |
Ref | Expression |
---|---|
nel0.1 |
Ref | Expression |
---|---|
nel0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eq0 3929 | . 2 | |
2 | nel0.1 | . 2 | |
3 | 1, 2 | mpgbir 1726 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wceq 1483 wcel 1990 c0 3915 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-v 3202 df-dif 3577 df-nul 3916 |
This theorem is referenced by: iun0 4576 0iun 4577 0xp 5199 dm0 5339 cnv0 5535 fzouzdisj 12504 bj-ccinftydisj 33100 finxp0 33228 stoweidlem44 40261 |
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