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Mirrors > Home > NFE 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 | pm4.61 415 |
. . 3
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2 | anclb 530 |
. . . . 5
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3 | elin 3220 |
. . . . . 6
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4 | 3 | imbi2i 303 |
. . . . 5
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5 | iman 413 |
. . . . 5
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6 | 2, 4, 5 | 3bitr2i 264 |
. . . 4
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7 | 6 | con2bii 322 |
. . 3
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8 | eldif 3222 |
. . 3
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9 | 1, 7, 8 | 3bitr4i 268 |
. 2
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10 | 9 | difeqri 3388 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2479 df-v 2862 df-nin 3212 df-compl 3213 df-in 3214 df-dif 3216 |
This theorem is referenced by: dfin4 3496 indif 3498 symdif1 3520 notrab 3533 |
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