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Mirrors > Home > ILE Home > Th. List > resundi | Unicode version |
Description: Distributive law for restriction over union. Theorem 31 of [Suppes] p. 65. (Contributed by NM, 30-Sep-2002.) |
Ref | Expression |
---|---|
resundi |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | xpundir 4554 |
. . . 4
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2 | 1 | ineq2i 3238 |
. . 3
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3 | indi 3287 |
. . 3
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4 | 2, 3 | eqtri 2133 |
. 2
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5 | df-res 4509 |
. 2
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6 | df-res 4509 |
. . 3
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7 | df-res 4509 |
. . 3
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8 | 6, 7 | uneq12i 3192 |
. 2
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9 | 4, 5, 8 | 3eqtr4i 2143 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 681 ax-5 1404 ax-7 1405 ax-gen 1406 ax-ie1 1450 ax-ie2 1451 ax-8 1463 ax-10 1464 ax-11 1465 ax-i12 1466 ax-bndl 1467 ax-4 1468 ax-17 1487 ax-i9 1491 ax-ial 1495 ax-i5r 1496 ax-ext 2095 |
This theorem depends on definitions: df-bi 116 df-tru 1315 df-nf 1418 df-sb 1717 df-clab 2100 df-cleq 2106 df-clel 2109 df-nfc 2242 df-v 2657 df-un 3039 df-in 3041 df-opab 3948 df-xp 4503 df-res 4509 |
This theorem is referenced by: imaundi 4907 relresfld 5024 relcoi1 5026 resasplitss 5258 fnsnsplitss 5571 fnsnsplitdc 6353 fnfi 6775 fseq1p1m1 9761 resunimafz0 10461 |
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