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Mirrors > Home > ILE Home > Th. List > dmresi | Unicode version |
Description: The domain of a restricted identity function. (Contributed by NM, 27-Aug-2004.) |
Ref | Expression |
---|---|
dmresi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssv 3170 | . . 3 | |
2 | dmi 4827 | . . 3 | |
3 | 1, 2 | sseqtrri 3183 | . 2 |
4 | ssdmres 4914 | . 2 | |
5 | 3, 4 | mpbi 144 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1349 cvv 2731 wss 3122 cid 4274 cdm 4612 cres 4614 |
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 705 ax-5 1441 ax-7 1442 ax-gen 1443 ax-ie1 1487 ax-ie2 1488 ax-8 1498 ax-10 1499 ax-11 1500 ax-i12 1501 ax-bndl 1503 ax-4 1504 ax-17 1520 ax-i9 1524 ax-ial 1528 ax-i5r 1529 ax-14 2145 ax-ext 2153 ax-sep 4108 ax-pow 4161 ax-pr 4195 |
This theorem depends on definitions: df-bi 116 df-3an 976 df-tru 1352 df-nf 1455 df-sb 1757 df-eu 2023 df-mo 2024 df-clab 2158 df-cleq 2164 df-clel 2167 df-nfc 2302 df-ral 2454 df-rex 2455 df-v 2733 df-un 3126 df-in 3128 df-ss 3135 df-pw 3569 df-sn 3590 df-pr 3591 df-op 3593 df-br 3991 df-opab 4052 df-id 4279 df-xp 4618 df-rel 4619 df-dm 4622 df-res 4624 |
This theorem is referenced by: fnresi 5317 iordsmo 6280 |
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