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Mirrors > Home > ILE Home > Th. List > dmiin | Unicode version |
Description: Domain of an intersection. (Contributed by FL, 15-Oct-2012.) |
Ref | Expression |
---|---|
dmiin |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfii1 3882 | . . . 4 | |
2 | 1 | nfdm 4832 | . . 3 |
3 | 2 | ssiinf 3900 | . 2 |
4 | iinss2 3903 | . . 3 | |
5 | dmss 4787 | . . 3 | |
6 | 4, 5 | syl 14 | . 2 |
7 | 3, 6 | mprgbir 2515 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 2128 wss 3102 ciin 3852 cdm 4588 |
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 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-v 2714 df-un 3106 df-in 3108 df-ss 3115 df-sn 3567 df-pr 3568 df-op 3570 df-iin 3854 df-br 3968 df-dm 4598 |
This theorem is referenced by: (None) |
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