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Mirrors > Home > ILE Home > Th. List > iinuniss | Unicode version |
Description: A relationship involving union and indexed intersection. Exercise 23 of [Enderton] p. 33 but with equality changed to subset. (Contributed by Jim Kingdon, 19-Aug-2018.) |
Ref | Expression |
---|---|
iinuniss |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | r19.32vr 2625 |
. . . 4
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2 | vex 2740 |
. . . . . 6
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3 | 2 | elint2 3851 |
. . . . 5
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4 | 3 | orbi2i 762 |
. . . 4
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5 | elun 3276 |
. . . . 5
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6 | 5 | ralbii 2483 |
. . . 4
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7 | 1, 4, 6 | 3imtr4i 201 |
. . 3
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8 | 7 | ss2abi 3227 |
. 2
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9 | df-un 3133 |
. 2
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10 | df-iin 3889 |
. 2
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11 | 8, 9, 10 | 3sstr4i 3196 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-v 2739 df-un 3133 df-in 3135 df-ss 3142 df-int 3845 df-iin 3889 |
This theorem is referenced by: (None) |
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