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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 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | inss1 3157 | . . 3 | |
2 | ssddif 3171 | . . 3 | |
3 | 1, 2 | mpbi 133 | . 2 |
4 | difin 3174 | . . 3 | |
5 | 4 | difeq2i 3059 | . 2 |
6 | 3, 5 | sseqtri 2977 | 1 |
Colors of variables: wff set class |
Syntax hints: cdif 2914 cin 2916 wss 2917 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-in1 544 ax-in2 545 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-fal 1249 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-rab 2315 df-v 2559 df-dif 2920 df-in 2924 df-ss 2931 |
This theorem is referenced by: (None) |
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