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Mirrors > Home > ILE Home > Th. List > renemnf | Unicode version |
Description: No real equals minus infinity. (Contributed by NM, 14-Oct-2005.) (Proof shortened by Andrew Salmon, 19-Nov-2011.) |
Ref | Expression |
---|---|
renemnf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mnfnre 7921 | . . . 4 | |
2 | 1 | neli 2424 | . . 3 |
3 | eleq1 2220 | . . 3 | |
4 | 2, 3 | mtbiri 665 | . 2 |
5 | 4 | necon2ai 2381 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1335 wcel 2128 wne 2327 cr 7732 cmnf 7911 |
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-ext 2139 ax-setind 4497 ax-cnex 7824 ax-resscn 7825 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 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-ral 2440 df-v 2714 df-dif 3104 df-un 3106 df-in 3108 df-ss 3115 df-pw 3545 df-sn 3566 df-pr 3567 df-uni 3774 df-pnf 7915 df-mnf 7916 |
This theorem is referenced by: renemnfd 7930 renfdisj 7938 ltxrlt 7944 xrnemnf 9685 xrlttri3 9705 ngtmnft 9722 xrrebnd 9724 rexneg 9735 xrmnfdc 9748 rexadd 9757 xaddnemnf 9762 xaddcom 9766 xaddid1 9767 xnegdi 9773 xpncan 9776 xleadd1a 9778 xltadd1 9781 xposdif 9787 xrmaxrecl 11156 isxmet2d 12790 |
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