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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 3347 | . . 3 | |
2 | ssddif 3361 | . . 3 | |
3 | 1, 2 | mpbi 144 | . 2 |
4 | difin 3364 | . . 3 | |
5 | 4 | difeq2i 3242 | . 2 |
6 | 3, 5 | sseqtri 3181 | 1 |
Colors of variables: wff set class |
Syntax hints: cdif 3118 cin 3120 wss 3121 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 609 ax-in2 610 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-fal 1354 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rab 2457 df-v 2732 df-dif 3123 df-in 3127 df-ss 3134 |
This theorem is referenced by: (None) |
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