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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 3942 |
. 2
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4 | 1, 2, 3 | syl2an 287 |
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-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-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-v 2691 df-un 3080 df-sn 3538 df-pr 3539 df-op 3541 df-br 3938 |
This theorem is referenced by: breqan12rd 3954 sosng 4620 isoresbr 5718 isoid 5719 isores3 5724 isoini2 5728 ofrfval 5998 oviec 6543 enqbreq2 7189 ltresr2 7672 axpre-ltadd 7718 leltadd 8233 xltneg 9649 lt2sq 10397 le2sq 10398 cnreim 10782 sqrtle 10840 sqrtlt 10841 absext 10867 reefiso 12906 logltb 13003 |
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