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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 4627 | . 2 | |
2 | brrelex2 4628 | . 2 | |
3 | simpr 109 | . 2 | |
4 | breldmg 4793 | . 2 | |
5 | 1, 2, 3, 4 | syl3anc 1220 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wcel 2128 cvv 2712 class class class wbr 3966 cdm 4587 wrel 4592 |
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 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-14 2131 ax-ext 2139 ax-sep 4083 ax-pow 4136 ax-pr 4170 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-v 2714 df-un 3106 df-in 3108 df-ss 3115 df-pw 3545 df-sn 3566 df-pr 3567 df-op 3569 df-br 3967 df-opab 4027 df-xp 4593 df-rel 4594 df-dm 4597 |
This theorem is referenced by: releldmb 4824 releldmi 4826 funeu 5196 fnbr 5273 relelfvdm 5501 funbrfv2b 5514 funfvbrb 5581 ercl 6492 dvidlemap 13102 dvmulxxbr 13108 dviaddf 13111 dvimulf 13112 dvcoapbr 13113 |
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