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Mirrors > Home > ILE Home > Th. List > releldmi | Unicode version |
Description: The first argument of a binary relation belongs to its domain. (Contributed by NM, 28-Apr-2015.) |
Ref | Expression |
---|---|
releldm.1 |
Ref | Expression |
---|---|
releldmi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | releldm.1 | . 2 | |
2 | releldm 4569 | . 2 | |
3 | 1, 2 | mpan 400 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 1393 class class class wbr 3764 cdm 4345 wrel 4350 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-14 1405 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-sep 3875 ax-pow 3927 ax-pr 3944 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-rex 2312 df-v 2559 df-un 2922 df-in 2924 df-ss 2931 df-pw 3361 df-sn 3381 df-pr 3382 df-op 3384 df-br 3765 df-opab 3819 df-xp 4351 df-rel 4352 df-dm 4355 |
This theorem is referenced by: iiserex 9859 climrecvg1n 9867 climcvg1nlem 9868 |
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