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Mirrors > Home > ILE Home > Th. List > releldmb | Unicode version |
Description: Membership in a domain. (Contributed by Mario Carneiro, 5-Nov-2015.) |
Ref | Expression |
---|---|
releldmb |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eldmg 4798 | . . 3 | |
2 | 1 | ibi 175 | . 2 |
3 | releldm 4838 | . . . 4 | |
4 | 3 | ex 114 | . . 3 |
5 | 4 | exlimdv 1807 | . 2 |
6 | 2, 5 | impbid2 142 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wex 1480 wcel 2136 class class class wbr 3981 cdm 4603 wrel 4608 |
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 1435 ax-7 1436 ax-gen 1437 ax-ie1 1481 ax-ie2 1482 ax-8 1492 ax-10 1493 ax-11 1494 ax-i12 1495 ax-bndl 1497 ax-4 1498 ax-17 1514 ax-i9 1518 ax-ial 1522 ax-i5r 1523 ax-14 2139 ax-ext 2147 ax-sep 4099 ax-pow 4152 ax-pr 4186 |
This theorem depends on definitions: df-bi 116 df-3an 970 df-tru 1346 df-nf 1449 df-sb 1751 df-clab 2152 df-cleq 2158 df-clel 2161 df-nfc 2296 df-ral 2448 df-rex 2449 df-v 2727 df-un 3119 df-in 3121 df-ss 3128 df-pw 3560 df-sn 3581 df-pr 3582 df-op 3584 df-br 3982 df-opab 4043 df-xp 4609 df-rel 4610 df-dm 4613 |
This theorem is referenced by: (None) |
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