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Mirrors > Home > ILE Home > Th. List > indir | Unicode version |
Description: Distributive law for intersection over union. Theorem 28 of [Suppes] p. 27. (Contributed by NM, 30-Sep-2002.) |
Ref | Expression |
---|---|
indir |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | indi 3382 |
. 2
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2 | incom 3327 |
. 2
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3 | incom 3327 |
. . 3
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4 | incom 3327 |
. . 3
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5 | 3, 4 | uneq12i 3287 |
. 2
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6 | 1, 2, 5 | 3eqtr4i 2208 |
1
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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 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-v 2739 df-un 3133 df-in 3135 |
This theorem is referenced by: difundir 3388 undisj1 3480 disjpr2 3656 resundir 4921 djuassen 7215 |
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