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Mirrors > Home > ILE Home > Th. List > breqtrrd | Unicode version |
Description: Substitution of equal classes into a binary relation. (Contributed by NM, 24-Oct-1999.) |
Ref | Expression |
---|---|
breqtrrd.1 |
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breqtrrd.2 |
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Ref | Expression |
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breqtrrd |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | breqtrrd.1 |
. 2
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2 | breqtrrd.2 |
. . 3
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3 | 2 | eqcomd 2042 |
. 2
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4 | 1, 3 | breqtrd 3779 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 629 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-10 1393 ax-11 1394 ax-i12 1395 ax-bndl 1396 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 |
This theorem depends on definitions: df-bi 110 df-3an 886 df-tru 1245 df-nf 1347 df-sb 1643 df-clab 2024 df-cleq 2030 df-clel 2033 df-nfc 2164 df-v 2553 df-un 2916 df-sn 3373 df-pr 3374 df-op 3376 df-br 3756 |
This theorem is referenced by: addlocprlemeq 6516 ltexprlemopl 6575 recexprlemloc 6603 cauappcvgprlemopl 6618 cauappcvgprlemladdfu 6626 cauappcvgprlem1 6631 caucvgprlemopl 6640 caucvgprlemladdfu 6648 mulgt0sr 6704 archsr 6708 mulap0r 7399 prodgt0 7599 uzsubsubfz 8681 fzctr 8761 leexp1a 8963 sqgt0ap 8975 sqge0 8983 nnlesq 9009 expnbnd 9025 cjmulge0 9117 |
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