Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > mnfnepnf | GIF 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 7934 | . 2 ⊢ +∞ ≠ -∞ | |
2 | 1 | necomi 2412 | 1 ⊢ -∞ ≠ +∞ |
Colors of variables: wff set class |
Syntax hints: ≠ wne 2327 +∞cpnf 7911 -∞cmnf 7912 |
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 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-13 2130 ax-14 2131 ax-ext 2139 ax-sep 4084 ax-pow 4137 ax-un 4395 ax-cnex 7825 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-fal 1341 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ne 2328 df-nel 2423 df-rex 2441 df-rab 2444 df-v 2714 df-un 3106 df-in 3108 df-ss 3115 df-pw 3546 df-sn 3567 df-pr 3568 df-uni 3775 df-pnf 7916 df-mnf 7917 df-xr 7918 |
This theorem is referenced by: xrnepnf 9691 xrlttri3 9710 nltpnft 9724 xnegmnf 9739 xrpnfdc 9752 xaddmnf1 9758 xaddmnf2 9759 mnfaddpnf 9761 xaddnepnf 9768 xsubge0 9791 xposdif 9792 xleaddadd 9797 |
Copyright terms: Public domain | W3C validator |