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Mirrors > Home > ILE Home > Th. List > brelrng | Unicode version |
Description: The second argument of a binary relation belongs to its range. (Contributed by NM, 29-Jun-2008.) |
Ref | Expression |
---|---|
brelrng |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | brcnvg 4767 | . . . . 5 | |
2 | 1 | ancoms 266 | . . . 4 |
3 | 2 | biimp3ar 1328 | . . 3 |
4 | breldmg 4792 | . . . 4 | |
5 | 4 | 3com12 1189 | . . 3 |
6 | 3, 5 | syld3an3 1265 | . 2 |
7 | df-rn 4597 | . 2 | |
8 | 6, 7 | eleqtrrdi 2251 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 w3a 963 wcel 2128 class class class wbr 3965 ccnv 4585 cdm 4586 crn 4587 |
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 4082 ax-pow 4135 ax-pr 4169 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 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 3966 df-opab 4026 df-cnv 4594 df-dm 4596 df-rn 4597 |
This theorem is referenced by: opelrng 4818 brelrn 4819 relelrn 4822 fvssunirng 5483 shftfvalg 10718 ovshftex 10719 shftfval 10721 |
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