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Mirrors > Home > MPE Home > Th. List > nemtbir | Structured version Visualization version Unicode version |
Description: An inference from an inequality, related to modus tollens. (Contributed by NM, 13-Apr-2007.) |
Ref | Expression |
---|---|
nemtbir.1 | |
nemtbir.2 |
Ref | Expression |
---|---|
nemtbir |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nemtbir.1 | . . 3 | |
2 | 1 | neii 2796 | . 2 |
3 | nemtbir.2 | . 2 | |
4 | 2, 3 | mtbir 313 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wb 196 wceq 1483 wne 2794 |
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-ne 2795 |
This theorem is referenced by: opthwiener 4976 opthprc 5167 snnen2o 8149 cfpwsdom 9406 m1exp1 15093 pmtrsn 17939 gzrngunitlem 19811 logbmpt 24526 ex-id 27291 ex-mod 27306 sltval2 31809 sltsolem1 31826 nolt02o 31845 clsk1indlem4 38342 clsk1indlem1 38343 etransc 40500 |
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