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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 7479 intqfrac2 10095 m1modge3gt1 10147 bernneq2 10416 reccn2ap 11085 eirraplem 11486 nno 11606 oddprmge3 11818 sqnprm 11819 oddennn 11908 strle2g 12053 strle3g 12054 1strstrg 12060 2strstrg 12062 rngstrg 12077 srngstrd 12084 lmodstrd 12095 ipsstrd 12103 topgrpstrd 12113 psmetge0 12503 cosq14gt0 12916 cosq34lt1 12934 pwf1oexmid 13197 trilpolemeq1 13236 |
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