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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 |
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eqbrtrid.2 |
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Ref | Expression |
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eqbrtrid |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqbrtrid.2 |
. 2
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2 | eqbrtrid.1 |
. 2
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3 | eqid 2193 |
. 2
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4 | 1, 2, 3 | 3brtr4g 4063 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2175 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2180 df-cleq 2186 df-clel 2189 df-nfc 2325 df-v 2762 df-un 3157 df-sn 3624 df-pr 3625 df-op 3627 df-br 4030 |
This theorem is referenced by: xp1en 6877 caucvgprlemm 7728 intqfrac2 10390 m1modge3gt1 10442 bernneq2 10732 reccn2ap 11456 eirraplem 11920 nno 12047 oddprmge3 12273 sqnprm 12274 4sqlem6 12521 4sqlem13m 12541 4sqlem16 12544 4sqlem17 12545 oddennn 12549 strle2g 12725 strle3g 12726 1strstrg 12734 2strstrg 12736 rngstrg 12752 srngstrd 12763 lmodstrd 12781 ipsstrd 12793 topgrpstrd 12813 znidom 14145 psmetge0 14499 reeff1olem 14906 cosq14gt0 14967 cosq34lt1 14985 ioocosf1o 14989 gausslemma2dlem0c 15167 gausslemma2dlem0e 15169 lgseisenlem1 15186 lgsquadlem1 15191 pwf1oexmid 15490 trilpolemeq1 15530 |
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