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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 4792 | . . . . 5 | |
2 | 1 | ancoms 266 | . . . 4 |
3 | 2 | biimp3ar 1341 | . . 3 |
4 | breldmg 4817 | . . . 4 | |
5 | 4 | 3com12 1202 | . . 3 |
6 | 3, 5 | syld3an3 1278 | . 2 |
7 | df-rn 4622 | . 2 | |
8 | 6, 7 | eleqtrrdi 2264 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 w3a 973 wcel 2141 class class class wbr 3989 ccnv 4610 cdm 4611 crn 4612 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-14 2144 ax-ext 2152 ax-sep 4107 ax-pow 4160 ax-pr 4194 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-v 2732 df-un 3125 df-in 3127 df-ss 3134 df-pw 3568 df-sn 3589 df-pr 3590 df-op 3592 df-br 3990 df-opab 4051 df-cnv 4619 df-dm 4621 df-rn 4622 |
This theorem is referenced by: opelrng 4843 brelrn 4844 relelrn 4847 fvssunirng 5511 shftfvalg 10782 ovshftex 10783 shftfval 10785 |
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