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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mnfnre 7996 |
. . . 4
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2 | 1 | neli 2444 |
. . 3
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3 | eleq1 2240 |
. . 3
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4 | 2, 3 | mtbiri 675 |
. 2
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5 | 4 | necon2ai 2401 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 614 ax-in2 615 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 ax-setind 4535 ax-cnex 7899 ax-resscn 7900 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ne 2348 df-nel 2443 df-ral 2460 df-v 2739 df-dif 3131 df-un 3133 df-in 3135 df-ss 3142 df-pw 3577 df-sn 3598 df-pr 3599 df-uni 3810 df-pnf 7990 df-mnf 7991 |
This theorem is referenced by: renemnfd 8005 renfdisj 8013 ltxrlt 8019 xrnemnf 9773 xrlttri3 9793 ngtmnft 9813 xrrebnd 9815 rexneg 9826 xrmnfdc 9839 rexadd 9848 xaddnemnf 9853 xaddcom 9857 xaddid1 9858 xnegdi 9864 xpncan 9867 xleadd1a 9869 xltadd1 9872 xposdif 9878 xrmaxrecl 11256 isxmet2d 13719 |
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