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| Mirrors > Home > ILE Home > Th. List > iunin1 | Unicode version | ||
| Description: Indexed union of intersection. Generalization of half of theorem "Distributive laws" in [Enderton] p. 30. Use uniiun 3981 to recover Enderton's theorem. (Contributed by Mario Carneiro, 30-Aug-2015.) |
| Ref | Expression |
|---|---|
| iunin1 |
|
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | iunin2 3991 |
. 2
| |
| 2 | incom 3365 |
. . . 4
| |
| 3 | 2 | a1i 9 |
. . 3
|
| 4 | 3 | iuneq2i 3945 |
. 2
|
| 5 | incom 3365 |
. 2
| |
| 6 | 1, 4, 5 | 3eqtr4i 2236 |
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-io 711 ax-5 1470 ax-7 1471 ax-gen 1472 ax-ie1 1516 ax-ie2 1517 ax-8 1527 ax-10 1528 ax-11 1529 ax-i12 1530 ax-bndl 1532 ax-4 1533 ax-17 1549 ax-i9 1553 ax-ial 1557 ax-i5r 1558 ax-ext 2187 |
| This theorem depends on definitions: df-bi 117 df-tru 1376 df-nf 1484 df-sb 1786 df-clab 2192 df-cleq 2198 df-clel 2201 df-nfc 2337 df-ral 2489 df-rex 2490 df-v 2774 df-in 3172 df-ss 3179 df-iun 3929 |
| This theorem is referenced by: 2iunin 3994 tgrest 14641 |
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