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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 4644 | . 2 | |
2 | brrelex2 4645 | . 2 | |
3 | simpr 109 | . 2 | |
4 | breldmg 4810 | . 2 | |
5 | 1, 2, 3, 4 | syl3anc 1228 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wcel 2136 cvv 2726 class class class wbr 3982 cdm 4604 wrel 4609 |
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 699 ax-5 1435 ax-7 1436 ax-gen 1437 ax-ie1 1481 ax-ie2 1482 ax-8 1492 ax-10 1493 ax-11 1494 ax-i12 1495 ax-bndl 1497 ax-4 1498 ax-17 1514 ax-i9 1518 ax-ial 1522 ax-i5r 1523 ax-14 2139 ax-ext 2147 ax-sep 4100 ax-pow 4153 ax-pr 4187 |
This theorem depends on definitions: df-bi 116 df-3an 970 df-tru 1346 df-nf 1449 df-sb 1751 df-clab 2152 df-cleq 2158 df-clel 2161 df-nfc 2297 df-ral 2449 df-rex 2450 df-v 2728 df-un 3120 df-in 3122 df-ss 3129 df-pw 3561 df-sn 3582 df-pr 3583 df-op 3585 df-br 3983 df-opab 4044 df-xp 4610 df-rel 4611 df-dm 4614 |
This theorem is referenced by: releldmb 4841 releldmi 4843 funeu 5213 fnbr 5290 relelfvdm 5518 funbrfv2b 5531 funfvbrb 5598 ercl 6512 dvidlemap 13310 dvmulxxbr 13316 dviaddf 13319 dvimulf 13320 dvcoapbr 13321 |
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