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Mirrors > Home > ILE Home > Th. List > xgepnf | Unicode version |
Description: An extended real which is greater than plus infinity is plus infinity. (Contributed by Thierry Arnoux, 18-Dec-2016.) |
Ref | Expression |
---|---|
xgepnf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pnfxr 7842 | . . 3 | |
2 | xrlenlt 7853 | . . 3 | |
3 | 1, 2 | mpan 421 | . 2 |
4 | nltpnft 9627 | . 2 | |
5 | 3, 4 | bitr4d 190 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wb 104 wceq 1332 wcel 1481 class class class wbr 3937 cpnf 7821 cxr 7823 clt 7824 cle 7825 |
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 604 ax-in2 605 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-13 1492 ax-14 1493 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-sep 4054 ax-pow 4106 ax-pr 4139 ax-un 4363 ax-setind 4460 ax-cnex 7735 ax-resscn 7736 ax-pre-ltirr 7756 |
This theorem depends on definitions: df-bi 116 df-3or 964 df-3an 965 df-tru 1335 df-fal 1338 df-nf 1438 df-sb 1737 df-eu 2003 df-mo 2004 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ne 2310 df-nel 2405 df-ral 2422 df-rex 2423 df-rab 2426 df-v 2691 df-dif 3078 df-un 3080 df-in 3082 df-ss 3089 df-pw 3517 df-sn 3538 df-pr 3539 df-op 3541 df-uni 3745 df-br 3938 df-opab 3998 df-xp 4553 df-cnv 4555 df-pnf 7826 df-mnf 7827 df-xr 7828 df-ltxr 7829 df-le 7830 |
This theorem is referenced by: xnn0lenn0nn0 9678 xleaddadd 9700 |
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