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Mirrors > Home > ILE Home > Th. List > breq12i | Unicode version |
Description: Equality inference for a binary relation. (Contributed by NM, 8-Feb-1996.) (Proof shortened by Eric Schmidt, 4-Apr-2007.) |
Ref | Expression |
---|---|
breq1i.1 |
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breq12i.2 |
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Ref | Expression |
---|---|
breq12i |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | breq1i.1 |
. 2
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2 | breq12i.2 |
. 2
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3 | breq12 4010 |
. 2
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4 | 1, 2, 3 | mp2an 426 |
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-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-v 2741 df-un 3135 df-sn 3600 df-pr 3601 df-op 3603 df-br 4006 |
This theorem is referenced by: 3brtr3g 4038 3brtr4g 4039 caovord2 6050 ltneg 8422 leneg 8425 inelr 8544 lt2sqi 10611 le2sqi 10612 |
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