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Mirrors > Home > ILE Home > Th. List > mnfnepnf | Unicode version |
Description: Minus and plus infinity are different (common case). (Contributed by David A. Wheeler, 8-Dec-2018.) |
Ref | Expression |
---|---|
mnfnepnf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pnfnemnf 7788 | . 2 | |
2 | 1 | necomi 2370 | 1 |
Colors of variables: wff set class |
Syntax hints: wne 2285 cpnf 7765 cmnf 7766 |
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 588 ax-in2 589 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-13 1476 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-pow 4068 ax-un 4325 ax-cnex 7679 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-fal 1322 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ne 2286 df-nel 2381 df-rex 2399 df-rab 2402 df-v 2662 df-un 3045 df-in 3047 df-ss 3054 df-pw 3482 df-sn 3503 df-pr 3504 df-uni 3707 df-pnf 7770 df-mnf 7771 df-xr 7772 |
This theorem is referenced by: xrnepnf 9533 xrlttri3 9551 nltpnft 9565 xnegmnf 9580 xrpnfdc 9593 xaddmnf1 9599 xaddmnf2 9600 mnfaddpnf 9602 xaddnepnf 9609 xsubge0 9632 xposdif 9633 xleaddadd 9638 |
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