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Mirrors > Home > ILE Home > Th. List > mnfnre | Unicode version |
Description: Minus infinity is not a real number. (Contributed by NM, 13-Oct-2005.) |
Ref | Expression |
---|---|
mnfnre |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cnex 7737 | . . . . 5 | |
2 | 2pwuninelg 6173 | . . . . 5 | |
3 | 1, 2 | ax-mp 5 | . . . 4 |
4 | df-mnf 7796 | . . . . . 6 | |
5 | df-pnf 7795 | . . . . . . 7 | |
6 | 5 | pweqi 3509 | . . . . . 6 |
7 | 4, 6 | eqtri 2158 | . . . . 5 |
8 | 7 | eleq1i 2203 | . . . 4 |
9 | 3, 8 | mtbir 660 | . . 3 |
10 | recn 7746 | . . 3 | |
11 | 9, 10 | mto 651 | . 2 |
12 | 11 | nelir 2404 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wcel 1480 wnel 2401 cvv 2681 cpw 3505 cuni 3731 cc 7611 cr 7612 cpnf 7790 cmnf 7791 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 603 ax-in2 604 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 ax-setind 4447 ax-cnex 7704 ax-resscn 7705 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-nel 2402 df-ral 2419 df-v 2683 df-dif 3068 df-un 3070 df-in 3072 df-ss 3079 df-pw 3507 df-sn 3528 df-pr 3529 df-uni 3732 df-pnf 7795 df-mnf 7796 |
This theorem is referenced by: renemnf 7807 xrltnr 9559 nltmnf 9567 |
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