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Mirrors > Home > ILE Home > Th. List > difin | Unicode version |
Description: Difference with intersection. Theorem 33 of [Suppes] p. 29. (Contributed by NM, 31-Mar-1998.) (Proof shortened by Andrew Salmon, 26-Jun-2011.) |
Ref | Expression |
---|---|
difin |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-in2 616 |
. . . . . . . 8
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2 | 1 | expd 258 |
. . . . . . 7
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3 | dfnot 1382 |
. . . . . . 7
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4 | 2, 3 | imbitrrdi 162 |
. . . . . 6
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5 | 4 | com12 30 |
. . . . 5
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6 | 5 | imdistani 445 |
. . . 4
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7 | simpr 110 |
. . . . . 6
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8 | 7 | con3i 633 |
. . . . 5
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9 | 8 | anim2i 342 |
. . . 4
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10 | 6, 9 | impbii 126 |
. . 3
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11 | eldif 3153 |
. . . 4
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12 | elin 3333 |
. . . . . 6
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13 | 12 | notbii 669 |
. . . . 5
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14 | 13 | anbi2i 457 |
. . . 4
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15 | 11, 14 | bitri 184 |
. . 3
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16 | eldif 3153 |
. . 3
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17 | 10, 15, 16 | 3bitr4i 212 |
. 2
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18 | 17 | eqriv 2186 |
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-v 2754 df-dif 3146 df-in 3150 |
This theorem is referenced by: inssddif 3391 symdif1 3415 notrab 3427 disjdif2 3516 unfiin 6955 bj-charfundcALT 15039 |
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