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Mirrors > Home > ILE Home > Th. List > difin2 | Unicode version |
Description: Represent a set difference as an intersection with a larger difference. (Contributed by Jeff Madsen, 2-Sep-2009.) |
Ref | Expression |
---|---|
difin2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssel 3164 |
. . . . 5
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2 | 1 | pm4.71d 393 |
. . . 4
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3 | 2 | anbi1d 465 |
. . 3
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4 | eldif 3153 |
. . 3
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5 | elin 3333 |
. . . 4
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6 | eldif 3153 |
. . . . 5
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7 | 6 | anbi1i 458 |
. . . 4
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8 | ancom 266 |
. . . . 5
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9 | anass 401 |
. . . . 5
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10 | 8, 9 | bitr4i 187 |
. . . 4
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11 | 5, 7, 10 | 3bitri 206 |
. . 3
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12 | 3, 4, 11 | 3bitr4g 223 |
. 2
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13 | 12 | 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-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-v 2754 df-dif 3146 df-in 3150 df-ss 3157 |
This theorem is referenced by: (None) |
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