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| Mirrors > Home > ILE Home > Th. List > mnfltpnf | Unicode version | ||
| Description: Minus infinity is less than plus infinity. (Contributed by NM, 14-Oct-2005.) |
| Ref | Expression |
|---|---|
| mnfltpnf |
|
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | eqid 2205 |
. . . 4
| |
| 2 | eqid 2205 |
. . . 4
| |
| 3 | olc 713 |
. . . 4
| |
| 4 | 1, 2, 3 | mp2an 426 |
. . 3
|
| 5 | 4 | orci 733 |
. 2
|
| 6 | mnfxr 8129 |
. . 3
| |
| 7 | pnfxr 8125 |
. . 3
| |
| 8 | ltxr 9897 |
. . 3
| |
| 9 | 6, 7, 8 | mp2an 426 |
. 2
|
| 10 | 5, 9 | mpbir 146 |
1
|
| 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-io 711 ax-5 1470 ax-7 1471 ax-gen 1472 ax-ie1 1516 ax-ie2 1517 ax-8 1527 ax-10 1528 ax-11 1529 ax-i12 1530 ax-bndl 1532 ax-4 1533 ax-17 1549 ax-i9 1553 ax-ial 1557 ax-i5r 1558 ax-13 2178 ax-14 2179 ax-ext 2187 ax-sep 4162 ax-pow 4218 ax-pr 4253 ax-un 4480 ax-cnex 8016 |
| This theorem depends on definitions: df-bi 117 df-3an 983 df-tru 1376 df-nf 1484 df-sb 1786 df-eu 2057 df-mo 2058 df-clab 2192 df-cleq 2198 df-clel 2201 df-nfc 2337 df-ral 2489 df-rex 2490 df-v 2774 df-un 3170 df-in 3172 df-ss 3179 df-pw 3618 df-sn 3639 df-pr 3640 df-op 3642 df-uni 3851 df-br 4045 df-opab 4106 df-xp 4681 df-pnf 8109 df-mnf 8110 df-xr 8111 df-ltxr 8112 |
| This theorem is referenced by: mnfltxr 9908 xrlttr 9917 xrltso 9918 xrlttri3 9919 nltpnft 9936 npnflt 9937 ngtmnft 9939 nmnfgt 9940 xltnegi 9957 xposdif 10004 |
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