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Mirrors > Home > ILE Home > Th. List > xnegmnf | Unicode version |
Description: Minus ![]() |
Ref | Expression |
---|---|
xnegmnf |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-xneg 9589 |
. 2
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2 | mnfnepnf 7845 |
. . 3
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3 | ifnefalse 3490 |
. . 3
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4 | 2, 3 | ax-mp 5 |
. 2
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5 | eqid 2140 |
. . 3
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6 | 5 | iftruei 3485 |
. 2
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7 | 1, 4, 6 | 3eqtri 2165 |
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 105 ax-ia2 106 ax-ia3 107 ax-in1 604 ax-in2 605 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-13 1492 ax-14 1493 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-sep 4054 ax-pow 4106 ax-un 4363 ax-cnex 7735 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-fal 1338 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ne 2310 df-nel 2405 df-rex 2423 df-rab 2426 df-v 2691 df-un 3080 df-in 3082 df-ss 3089 df-if 3480 df-pw 3517 df-sn 3538 df-pr 3539 df-uni 3745 df-pnf 7826 df-mnf 7827 df-xr 7828 df-xneg 9589 |
This theorem is referenced by: xnegcl 9645 xnegneg 9646 xltnegi 9648 xnegid 9672 xnegdi 9681 xsubge0 9694 xposdif 9695 |
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