Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 3327 | . . 3 | |
2 | ssddif 3341 | . . 3 | |
3 | 1, 2 | mpbi 144 | . 2 |
4 | difin 3344 | . . 3 | |
5 | 4 | difeq2i 3222 | . 2 |
6 | 3, 5 | sseqtri 3162 | 1 |
Colors of variables: wff set class |
Syntax hints: cdif 3099 cin 3101 wss 3102 |
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 604 ax-in2 605 ax-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-fal 1341 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rab 2444 df-v 2714 df-dif 3104 df-in 3108 df-ss 3115 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |