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Mirrors > Home > ILE Home > Th. List > releldm | Unicode version |
Description: The first argument of a binary relation belongs to its domain. (Contributed by NM, 2-Jul-2008.) |
Ref | Expression |
---|---|
releldm |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | brrelex 4579 | . 2 | |
2 | brrelex2 4580 | . 2 | |
3 | simpr 109 | . 2 | |
4 | breldmg 4745 | . 2 | |
5 | 1, 2, 3, 4 | syl3anc 1216 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wcel 1480 cvv 2686 class class class wbr 3929 cdm 4539 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-ral 2421 df-rex 2422 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-br 3930 df-opab 3990 df-xp 4545 df-rel 4546 df-dm 4549 |
This theorem is referenced by: releldmb 4776 releldmi 4778 funeu 5148 fnbr 5225 relelfvdm 5453 funbrfv2b 5466 funfvbrb 5533 ercl 6440 dvidlemap 12829 dvmulxxbr 12835 dviaddf 12838 dvimulf 12839 dvcoapbr 12840 |
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