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Mirrors > Home > ILE Home > Th. List > reldom | GIF version |
Description: Dominance is a relation. (Contributed by NM, 28-Mar-1998.) |
Ref | Expression |
---|---|
reldom | ⊢ Rel ≼ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-dom 6566 | . 2 ⊢ ≼ = {〈𝑥, 𝑦〉 ∣ ∃𝑓 𝑓:𝑥–1-1→𝑦} | |
2 | 1 | relopabi 4603 | 1 ⊢ Rel ≼ |
Colors of variables: wff set class |
Syntax hints: ∃wex 1436 Rel wrel 4482 –1-1→wf1 5056 ≼ cdom 6563 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 671 ax-5 1391 ax-7 1392 ax-gen 1393 ax-ie1 1437 ax-ie2 1438 ax-8 1450 ax-10 1451 ax-11 1452 ax-i12 1453 ax-bndl 1454 ax-4 1455 ax-14 1460 ax-17 1474 ax-i9 1478 ax-ial 1482 ax-i5r 1483 ax-ext 2082 ax-sep 3986 ax-pow 4038 ax-pr 4069 |
This theorem depends on definitions: df-bi 116 df-3an 932 df-tru 1302 df-nf 1405 df-sb 1704 df-clab 2087 df-cleq 2093 df-clel 2096 df-nfc 2229 df-ral 2380 df-rex 2381 df-v 2643 df-un 3025 df-in 3027 df-ss 3034 df-pw 3459 df-sn 3480 df-pr 3481 df-op 3483 df-opab 3930 df-xp 4483 df-rel 4484 df-dom 6566 |
This theorem is referenced by: brdomg 6572 brdomi 6573 ctex 6577 domtr 6609 xpdom2 6654 xpdom1g 6656 mapdom1g 6670 isbth 6783 djudom 6893 difinfsn 6900 hashinfom 10365 |
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