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Mirrors > Home > ILE Home > Th. List > iindif2m | Unicode version |
Description: Indexed intersection of class difference. Compare to Theorem "De Morgan's laws" in [Enderton] p. 31. (Contributed by Jim Kingdon, 17-Aug-2018.) |
Ref | Expression |
---|---|
iindif2m |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | r19.28mv 3530 |
. . . 4
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2 | eldif 3153 |
. . . . . 6
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3 | 2 | bicomi 132 |
. . . . 5
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4 | 3 | ralbii 2496 |
. . . 4
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5 | ralnex 2478 |
. . . . . 6
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6 | eliun 3905 |
. . . . . 6
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7 | 5, 6 | xchbinxr 684 |
. . . . 5
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8 | 7 | anbi2i 457 |
. . . 4
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9 | 1, 4, 8 | 3bitr3g 222 |
. . 3
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10 | vex 2755 |
. . . 4
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11 | eliin 3906 |
. . . 4
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12 | 10, 11 | ax-mp 5 |
. . 3
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13 | eldif 3153 |
. . 3
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14 | 9, 12, 13 | 3bitr4g 223 |
. 2
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15 | 14 | eqrdv 2187 |
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-in1 615 ax-in2 616 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-fal 1370 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-v 2754 df-dif 3146 df-iun 3903 df-iin 3904 |
This theorem is referenced by: (None) |
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