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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 | |
breq12i.2 |
Ref | Expression |
---|---|
breq12i |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | breq1i.1 | . 2 | |
2 | breq12i.2 | . 2 | |
3 | breq12 3934 | . 2 | |
4 | 1, 2, 3 | mp2an 422 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 wceq 1331 class class class wbr 3929 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-v 2688 df-un 3075 df-sn 3533 df-pr 3534 df-op 3536 df-br 3930 |
This theorem is referenced by: 3brtr3g 3961 3brtr4g 3962 caovord2 5943 ltneg 8224 leneg 8227 inelr 8346 lt2sqi 10380 le2sqi 10381 |
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