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Mirrors > Home > ILE Home > Th. List > mnfltpnf | Unicode version |
Description: Minus infinity is less than plus infinity. (Contributed by NM, 14-Oct-2005.) |
Ref | Expression |
---|---|
mnfltpnf |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid 2187 |
. . . 4
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2 | eqid 2187 |
. . . 4
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3 | olc 712 |
. . . 4
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4 | 1, 2, 3 | mp2an 426 |
. . 3
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5 | 4 | orci 732 |
. 2
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6 | mnfxr 8027 |
. . 3
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7 | pnfxr 8023 |
. . 3
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8 | ltxr 9788 |
. . 3
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9 | 6, 7, 8 | mp2an 426 |
. 2
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10 | 5, 9 | mpbir 146 |
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-io 710 ax-5 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-10 1515 ax-11 1516 ax-i12 1517 ax-bndl 1519 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 ax-13 2160 ax-14 2161 ax-ext 2169 ax-sep 4133 ax-pow 4186 ax-pr 4221 ax-un 4445 ax-cnex 7915 |
This theorem depends on definitions: df-bi 117 df-3an 981 df-tru 1366 df-nf 1471 df-sb 1773 df-eu 2039 df-mo 2040 df-clab 2174 df-cleq 2180 df-clel 2183 df-nfc 2318 df-ral 2470 df-rex 2471 df-v 2751 df-un 3145 df-in 3147 df-ss 3154 df-pw 3589 df-sn 3610 df-pr 3611 df-op 3613 df-uni 3822 df-br 4016 df-opab 4077 df-xp 4644 df-pnf 8007 df-mnf 8008 df-xr 8009 df-ltxr 8010 |
This theorem is referenced by: mnfltxr 9799 xrlttr 9808 xrltso 9809 xrlttri3 9810 nltpnft 9827 npnflt 9828 ngtmnft 9830 nmnfgt 9831 xltnegi 9848 xposdif 9895 |
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