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Mirrors > Home > ILE Home > Th. List > xnegeq | Unicode version |
Description: Equality of two extended
numbers with ![]() ![]() |
Ref | Expression |
---|---|
xnegeq |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqeq1 2184 |
. . 3
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2 | eqeq1 2184 |
. . . 4
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3 | negeq 8146 |
. . . 4
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4 | 2, 3 | ifbieq2d 3558 |
. . 3
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5 | 1, 4 | ifbieq2d 3558 |
. 2
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6 | df-xneg 9768 |
. 2
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7 | df-xneg 9768 |
. 2
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8 | 5, 6, 7 | 3eqtr4g 2235 |
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 |
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-rex 2461 df-rab 2464 df-v 2739 df-un 3133 df-if 3535 df-sn 3598 df-pr 3599 df-op 3601 df-uni 3810 df-br 4003 df-iota 5177 df-fv 5223 df-ov 5875 df-neg 8127 df-xneg 9768 |
This theorem is referenced by: xnegcl 9828 xnegneg 9829 xneg11 9830 xltnegi 9831 xnegid 9855 xnegdi 9864 xsubge0 9877 xposdif 9878 xlesubadd 9879 xrnegiso 11263 infxrnegsupex 11264 xrminmax 11266 xrminrecl 11274 xrminadd 11276 xblss2ps 13775 xblss2 13776 |
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