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Mirrors > Home > ILE Home > Th. List > invdif | Unicode version |
Description: Intersection with universal complement. Remark in [Stoll] p. 20. (Contributed by NM, 17-Aug-2004.) |
Ref | Expression |
---|---|
invdif |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 2755 |
. . . . 5
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2 | eldif 3153 |
. . . . 5
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3 | 1, 2 | mpbiran 942 |
. . . 4
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4 | 3 | anbi2i 457 |
. . 3
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5 | elin 3333 |
. . 3
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6 | eldif 3153 |
. . 3
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7 | 4, 5, 6 | 3bitr4i 212 |
. 2
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8 | 7 | 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-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: indif2 3394 difundir 3403 difindir 3405 difdif2ss 3407 difun1 3410 difdifdirss 3522 nn0supp 9257 |
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