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Mirrors > Home > ILE Home > Th. List > inass | Unicode version |
Description: Associative law for intersection of classes. Exercise 9 of [TakeutiZaring] p. 17. (Contributed by NM, 3-May-1994.) |
Ref | Expression |
---|---|
inass |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | anass 396 |
. . . 4
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2 | elin 3225 |
. . . . 5
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3 | 2 | anbi2i 450 |
. . . 4
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4 | 1, 3 | bitr4i 186 |
. . 3
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5 | elin 3225 |
. . . 4
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6 | 5 | anbi1i 451 |
. . 3
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7 | elin 3225 |
. . 3
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8 | 4, 6, 7 | 3bitr4i 211 |
. 2
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9 | 8 | ineqri 3235 |
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 1406 ax-7 1407 ax-gen 1408 ax-ie1 1452 ax-ie2 1453 ax-8 1465 ax-10 1466 ax-11 1467 ax-i12 1468 ax-bndl 1469 ax-4 1470 ax-17 1489 ax-i9 1493 ax-ial 1497 ax-i5r 1498 ax-ext 2097 |
This theorem depends on definitions: df-bi 116 df-tru 1317 df-nf 1420 df-sb 1719 df-clab 2102 df-cleq 2108 df-clel 2111 df-nfc 2244 df-v 2659 df-in 3043 |
This theorem is referenced by: in12 3253 in32 3254 in4 3258 indif2 3286 difun1 3302 dfrab3ss 3320 resres 4789 inres 4794 imainrect 4942 restco 12186 restopnb 12193 |
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