![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
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 7005 |
. . . . 5
![]() ![]() ![]() ![]() | |
2 | 2pwuninelg 5898 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
3 | 1, 2 | ax-mp 7 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
4 | df-mnf 7063 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() | |
5 | df-pnf 7062 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() | |
6 | 5 | pweqi 3363 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
7 | 4, 6 | eqtri 2060 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
8 | 7 | eleq1i 2103 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
9 | 3, 8 | mtbir 596 |
. . 3
![]() ![]() ![]() ![]() ![]() |
10 | recn 7014 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
11 | 9, 10 | mto 588 |
. 2
![]() ![]() ![]() ![]() ![]() |
12 | 11 | nelir 2300 |
1
![]() ![]() ![]() ![]() |
Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-in1 544 ax-in2 545 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-setind 4262 ax-cnex 6975 ax-resscn 6976 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-nel 2207 df-ral 2311 df-v 2559 df-dif 2920 df-un 2922 df-in 2924 df-ss 2931 df-pw 3361 df-sn 3381 df-pr 3382 df-uni 3581 df-pnf 7062 df-mnf 7063 |
This theorem is referenced by: renemnf 7074 xrltnr 8701 nltmnf 8709 |
Copyright terms: Public domain | W3C validator |