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Mirrors > Home > ILE Home > Th. List > eqbrtrid | Unicode version |
Description: B chained equality inference for a binary relation. (Contributed by NM, 11-Oct-1999.) |
Ref | Expression |
---|---|
eqbrtrid.1 | |
eqbrtrid.2 |
Ref | Expression |
---|---|
eqbrtrid |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqbrtrid.2 | . 2 | |
2 | eqbrtrid.1 | . 2 | |
3 | eqid 2139 | . 2 | |
4 | 1, 2, 3 | 3brtr4g 3962 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 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: xp1en 6717 caucvgprlemm 7476 intqfrac2 10092 m1modge3gt1 10144 bernneq2 10413 reccn2ap 11082 eirraplem 11483 nno 11603 oddprmge3 11815 sqnprm 11816 oddennn 11905 strle2g 12050 strle3g 12051 1strstrg 12057 2strstrg 12059 rngstrg 12074 srngstrd 12081 lmodstrd 12092 ipsstrd 12100 topgrpstrd 12110 psmetge0 12500 cosq14gt0 12913 cosq34lt1 12931 pwf1oexmid 13194 trilpolemeq1 13233 |
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