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Mirrors > Home > ILE Home > Th. List > renemnf | Unicode version |
Description: No real equals minus infinity. (Contributed by NM, 14-Oct-2005.) (Proof shortened by Andrew Salmon, 19-Nov-2011.) |
Ref | Expression |
---|---|
renemnf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mnfnre 7161 | . . . 4 | |
2 | 1 | neli 2341 | . . 3 |
3 | eleq1 2141 | . . 3 | |
4 | 2, 3 | mtbiri 632 | . 2 |
5 | 4 | necon2ai 2299 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1284 wcel 1433 wne 2245 cr 6980 cmnf 7151 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 576 ax-in2 577 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-setind 4280 ax-cnex 7067 ax-resscn 7068 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ne 2246 df-nel 2340 df-ral 2353 df-v 2603 df-dif 2975 df-un 2977 df-in 2979 df-ss 2986 df-pw 3384 df-sn 3404 df-pr 3405 df-uni 3602 df-pnf 7155 df-mnf 7156 |
This theorem is referenced by: renemnfd 7170 renfdisj 7172 ltxrlt 7178 xrnemnf 8853 xrlttri3 8872 ngtmnft 8885 xrrebnd 8886 rexneg 8897 |
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