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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 3373 | 
. . . 4
 | |
| 2 | invdif 3405 | 
. . . 4
 | |
| 3 | 1, 2 | eqtr3i 2219 | 
. . 3
 | 
| 4 | undm 3421 | 
. . . . 5
 | |
| 5 | 4 | ineq2i 3361 | 
. . . 4
 | 
| 6 | invdif 3405 | 
. . . 4
 | |
| 7 | 5, 6 | eqtr3i 2219 | 
. . 3
 | 
| 8 | 3, 7 | eqtr3i 2219 | 
. 2
 | 
| 9 | invdif 3405 | 
. . 3
 | |
| 10 | 9 | difeq1i 3277 | 
. 2
 | 
| 11 | 8, 10 | eqtr3i 2219 | 
1
 | 
| Colors of variables: wff set class | 
| Syntax hints:     | 
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 615 ax-in2 616 ax-io 710 ax-5 1461 ax-7 1462 ax-gen 1463 ax-ie1 1507 ax-ie2 1508 ax-8 1518 ax-10 1519 ax-11 1520 ax-i12 1521 ax-bndl 1523 ax-4 1524 ax-17 1540 ax-i9 1544 ax-ial 1548 ax-i5r 1549 ax-ext 2178 | 
| This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1475 df-sb 1777 df-clab 2183 df-cleq 2189 df-clel 2192 df-nfc 2328 df-rab 2484 df-v 2765 df-dif 3159 df-un 3161 df-in 3163 | 
| This theorem is referenced by: dif32 3426 difabs 3427 difpr 3764 diffifi 6955 difinfinf 7167 | 
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