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Mirrors > Home > ILE Home > Th. List > difun1 | Unicode version |
Description: A relationship involving double difference and union. (Contributed by NM, 29-Aug-2004.) |
Ref | Expression |
---|---|
difun1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | inass 3176 | . . . 4 | |
2 | invdif 3206 | . . . 4 | |
3 | 1, 2 | eqtr3i 2103 | . . 3 |
4 | undm 3222 | . . . . 5 | |
5 | 4 | ineq2i 3164 | . . . 4 |
6 | invdif 3206 | . . . 4 | |
7 | 5, 6 | eqtr3i 2103 | . . 3 |
8 | 3, 7 | eqtr3i 2103 | . 2 |
9 | invdif 3206 | . . 3 | |
10 | 9 | difeq1i 3086 | . 2 |
11 | 8, 10 | eqtr3i 2103 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1284 cvv 2601 cdif 2970 cun 2971 cin 2972 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 576 ax-in2 577 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-rab 2357 df-v 2603 df-dif 2975 df-un 2977 df-in 2979 |
This theorem is referenced by: dif32 3227 difabs 3228 diffifi 6378 |
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