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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 3147 | . . . 4 | |
2 | invdif 3179 | . . . 4 | |
3 | 1, 2 | eqtr3i 2062 | . . 3 |
4 | undm 3195 | . . . . 5 | |
5 | 4 | ineq2i 3135 | . . . 4 |
6 | invdif 3179 | . . . 4 | |
7 | 5, 6 | eqtr3i 2062 | . . 3 |
8 | 3, 7 | eqtr3i 2062 | . 2 |
9 | invdif 3179 | . . 3 | |
10 | 9 | difeq1i 3058 | . 2 |
11 | 8, 10 | eqtr3i 2062 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1243 cvv 2557 cdif 2914 cun 2915 cin 2916 |
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-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-rab 2315 df-v 2559 df-dif 2920 df-un 2922 df-in 2924 |
This theorem is referenced by: dif32 3200 difabs 3201 diffifi 6351 |
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