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Mirrors > Home > MPE Home > Th. List > mnfnepnf | Structured version Visualization version 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 10094 | . 2 | |
2 | 1 | necomi 2848 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wne 2794 cpnf 10071 cmnf 10072 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-8 1992 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-pow 4843 ax-un 6949 ax-cnex 9992 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 df-nel 2898 df-rex 2918 df-rab 2921 df-v 3202 df-un 3579 df-in 3581 df-ss 3588 df-pw 4160 df-sn 4178 df-pr 4180 df-uni 4437 df-pnf 10076 df-mnf 10077 df-xr 10078 |
This theorem is referenced by: xrnepnf 11952 xnegmnf 12041 xaddmnf1 12059 xaddmnf2 12060 mnfaddpnf 12062 xaddnepnf 12068 xmullem2 12095 xadddilem 12124 resup 12666 |
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