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Mirrors > Home > ILE Home > Th. List > brdomi | Unicode version |
Description: Dominance relation. (Contributed by Mario Carneiro, 26-Apr-2015.) |
Ref | Expression |
---|---|
brdomi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | reldom 6702 | . . . 4 | |
2 | 1 | brrelex2i 4642 | . . 3 |
3 | brdomg 6705 | . . 3 | |
4 | 2, 3 | syl 14 | . 2 |
5 | 4 | ibi 175 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wex 1479 wcel 2135 cvv 2721 class class class wbr 3976 wf1 5179 cdom 6696 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-13 2137 ax-14 2138 ax-ext 2146 ax-sep 4094 ax-pow 4147 ax-pr 4181 ax-un 4405 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-v 2723 df-un 3115 df-in 3117 df-ss 3124 df-pw 3555 df-sn 3576 df-pr 3577 df-op 3579 df-uni 3784 df-br 3977 df-opab 4038 df-xp 4604 df-rel 4605 df-cnv 4606 df-dm 4608 df-rn 4609 df-fn 5185 df-f 5186 df-f1 5187 df-dom 6699 |
This theorem is referenced by: 2dom 6762 xpdom2 6788 dom0 6795 isinfinf 6854 infm 6861 djudom 7049 difinfsn 7056 exmidfodomrlemim 7148 |
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