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Mirrors > Home > ILE Home > Th. List > pnfnemnf | Unicode version |
Description: Plus and minus infinity
are different elements of ![]() |
Ref | Expression |
---|---|
pnfnemnf |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pnfxr 8008 |
. . . 4
![]() ![]() ![]() ![]() | |
2 | pwne 4160 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
3 | 1, 2 | ax-mp 5 |
. . 3
![]() ![]() ![]() ![]() ![]() |
4 | 3 | necomi 2432 |
. 2
![]() ![]() ![]() ![]() ![]() |
5 | df-mnf 7993 |
. 2
![]() ![]() ![]() ![]() ![]() | |
6 | 4, 5 | neeqtrri 2376 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 614 ax-in2 615 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-13 2150 ax-14 2151 ax-ext 2159 ax-sep 4121 ax-pow 4174 ax-un 4433 ax-cnex 7901 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-fal 1359 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ne 2348 df-nel 2443 df-rex 2461 df-rab 2464 df-v 2739 df-un 3133 df-in 3135 df-ss 3142 df-pw 3577 df-sn 3598 df-pr 3599 df-uni 3810 df-pnf 7992 df-mnf 7993 df-xr 7994 |
This theorem is referenced by: mnfnepnf 8011 xnn0nemnf 9248 xrnemnf 9775 xrltnr 9777 pnfnlt 9785 nltmnf 9786 ngtmnft 9815 xrmnfdc 9841 xaddpnf1 9844 xaddnemnf 9855 xposdif 9880 xleaddadd 9885 |
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