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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 3970 | . 2 | |
4 | 1, 2, 3 | mp2an 423 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 wceq 1335 class class class wbr 3965 |
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 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-v 2714 df-un 3106 df-sn 3566 df-pr 3567 df-op 3569 df-br 3966 |
This theorem is referenced by: 3brtr3g 3997 3brtr4g 3998 caovord2 5993 ltneg 8337 leneg 8340 inelr 8459 lt2sqi 10506 le2sqi 10507 |
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