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Mirrors > Home > ILE Home > Th. List > breqan12d | Unicode version |
Description: Equality deduction for a binary relation. (Contributed by NM, 8-Feb-1996.) |
Ref | Expression |
---|---|
breq1d.1 |
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breqan12i.2 |
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Ref | Expression |
---|---|
breqan12d |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | breq1d.1 |
. 2
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2 | breqan12i.2 |
. 2
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3 | breq12 3856 |
. 2
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4 | 1, 2, 3 | syl2an 284 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 666 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-10 1442 ax-11 1443 ax-i12 1444 ax-bndl 1445 ax-4 1446 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 |
This theorem depends on definitions: df-bi 116 df-3an 927 df-tru 1293 df-nf 1396 df-sb 1694 df-clab 2076 df-cleq 2082 df-clel 2085 df-nfc 2218 df-v 2622 df-un 3004 df-sn 3456 df-pr 3457 df-op 3459 df-br 3852 |
This theorem is referenced by: breqan12rd 3867 sosng 4524 isoresbr 5602 isoid 5603 isores3 5608 isoini2 5612 ofrfval 5878 oviec 6412 enqbreq2 6977 ltresr2 7438 axpre-ltadd 7482 leltadd 7986 xltneg 9359 lt2sq 10089 le2sq 10090 sqrtle 10530 sqrtlt 10531 absext 10557 |
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