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Mirrors > Home > MPE Home > Th. List > mnfnepnf | Structured version Visualization version GIF version |
Description: Minus and plus infinity are different. (Contributed by David A. Wheeler, 8-Dec-2018.) |
Ref | Expression |
---|---|
mnfnepnf | ⊢ -∞ ≠ +∞ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pnfnemnf 10684 | . 2 ⊢ +∞ ≠ -∞ | |
2 | 1 | necomi 3067 | 1 ⊢ -∞ ≠ +∞ |
Colors of variables: wff setvar class |
Syntax hints: ≠ wne 3013 +∞cpnf 10660 -∞cmnf 10661 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 ax-5 1902 ax-6 1961 ax-7 2006 ax-8 2107 ax-9 2115 ax-10 2136 ax-11 2151 ax-12 2167 ax-ext 2790 ax-sep 5194 ax-pow 5257 ax-un 7450 ax-cnex 10581 |
This theorem depends on definitions: df-bi 208 df-an 397 df-or 842 df-tru 1531 df-ex 1772 df-nf 1776 df-sb 2061 df-clab 2797 df-cleq 2811 df-clel 2890 df-nfc 2960 df-ne 3014 df-rex 3141 df-rab 3144 df-v 3494 df-un 3938 df-in 3940 df-ss 3949 df-pw 4537 df-sn 4558 df-pr 4560 df-uni 4831 df-pnf 10665 df-mnf 10666 df-xr 10667 |
This theorem is referenced by: xrnepnf 12501 xnegmnf 12591 xaddmnf1 12609 xaddmnf2 12610 mnfaddpnf 12612 xaddnepnf 12618 xmullem2 12646 xadddilem 12675 resup 13223 |
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