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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 3872 |
. 2
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4 | 1, 2, 3 | mp2an 418 |
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 668 ax-5 1388 ax-7 1389 ax-gen 1390 ax-ie1 1434 ax-ie2 1435 ax-8 1447 ax-10 1448 ax-11 1449 ax-i12 1450 ax-bndl 1451 ax-4 1452 ax-17 1471 ax-i9 1475 ax-ial 1479 ax-i5r 1480 ax-ext 2077 |
This theorem depends on definitions: df-bi 116 df-3an 929 df-tru 1299 df-nf 1402 df-sb 1700 df-clab 2082 df-cleq 2088 df-clel 2091 df-nfc 2224 df-v 2635 df-un 3017 df-sn 3472 df-pr 3473 df-op 3475 df-br 3868 |
This theorem is referenced by: 3brtr3g 3898 3brtr4g 3899 caovord2 5855 ltneg 8037 leneg 8040 inelr 8158 lt2sqi 10173 le2sqi 10174 |
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