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Mirrors > Home > ILE Home > Th. List > inssddif | Unicode version |
Description: Intersection of two classes and class difference. In classical logic, such as Exercise 4.10(q) of [Mendelson] p. 231, this is an equality rather than subset. (Contributed by Jim Kingdon, 26-Jul-2018.) |
Ref | Expression |
---|---|
inssddif |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | inss1 3221 |
. . 3
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2 | ssddif 3234 |
. . 3
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3 | 1, 2 | mpbi 144 |
. 2
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4 | difin 3237 |
. . 3
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5 | 4 | difeq2i 3116 |
. 2
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6 | 3, 5 | sseqtri 3059 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 580 ax-in2 581 ax-io 666 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-10 1442 ax-11 1443 ax-i12 1444 ax-bndl 1445 ax-4 1446 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 |
This theorem depends on definitions: df-bi 116 df-tru 1293 df-fal 1296 df-nf 1396 df-sb 1694 df-clab 2076 df-cleq 2082 df-clel 2085 df-nfc 2218 df-ral 2365 df-rab 2369 df-v 2622 df-dif 3002 df-in 3006 df-ss 3013 |
This theorem is referenced by: (None) |
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