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Mirrors > Home > MPE Home > Th. List > elnelall | Structured version Visualization version Unicode version |
Description: A contradiction concerning membership implies anything. (Contributed by Alexander van der Vekens, 25-Jan-2018.) |
Ref | Expression |
---|---|
elnelall |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-nel 2898 | . 2 | |
2 | pm2.24 121 | . 2 | |
3 | 1, 2 | syl5bi 232 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wcel 1990 wnel 2897 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 197 df-nel 2898 |
This theorem is referenced by: xnn0lenn0nn0 12075 |
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