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Mirrors > Home > ILE Home > Th. List > difdif2ss | Unicode version |
Description: Set difference with a set difference. In classical logic this would be equality rather than subset. (Contributed by Jim Kingdon, 27-Jul-2018.) |
Ref | Expression |
---|---|
difdif2ss |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | inssdif 3386 |
. . . 4
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2 | unss2 3321 |
. . . 4
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3 | 1, 2 | ax-mp 5 |
. . 3
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4 | difindiss 3404 |
. . 3
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5 | 3, 4 | sstri 3179 |
. 2
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6 | invdif 3392 |
. . . 4
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7 | 6 | eqcomi 2193 |
. . 3
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8 | 7 | difeq2i 3265 |
. 2
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9 | 5, 8 | sseqtrri 3205 |
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-ral 2473 df-rab 2477 df-v 2754 df-dif 3146 df-un 3148 df-in 3150 df-ss 3157 |
This theorem is referenced by: (None) |
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