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Mirrors > Home > ILE Home > Th. List > eqrelrdv | Unicode version |
Description: Deduce equality of relations from equivalence of membership. (Contributed by Rodolfo Medina, 10-Oct-2010.) |
Ref | Expression |
---|---|
eqrelrdv.1 | |
eqrelrdv.2 | |
eqrelrdv.3 |
Ref | Expression |
---|---|
eqrelrdv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqrelrdv.3 | . . 3 | |
2 | 1 | alrimivv 1847 | . 2 |
3 | eqrelrdv.1 | . . 3 | |
4 | eqrelrdv.2 | . . 3 | |
5 | eqrel 4628 | . . 3 | |
6 | 3, 4, 5 | mp2an 422 | . 2 |
7 | 2, 6 | sylibr 133 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wal 1329 wceq 1331 wcel 1480 cop 3530 wrel 4544 |
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-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-pow 4098 ax-pr 4131 |
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-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-opab 3990 df-xp 4545 df-rel 4546 |
This theorem is referenced by: eqbrrdiv 4637 fcnvres 5306 fmptco 5586 fisumcom2 11207 |
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