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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 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | anass 399 | . . . 4 | |
2 | elin 3300 | . . . . 5 | |
3 | 2 | anbi2i 453 | . . . 4 |
4 | 1, 3 | bitr4i 186 | . . 3 |
5 | elin 3300 | . . . 4 | |
6 | 5 | anbi1i 454 | . . 3 |
7 | elin 3300 | . . 3 | |
8 | 4, 6, 7 | 3bitr4i 211 | . 2 |
9 | 8 | ineqri 3310 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wceq 1342 wcel 2135 cin 3110 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-v 2723 df-in 3117 |
This theorem is referenced by: in12 3328 in32 3329 in4 3333 indif2 3361 difun1 3377 dfrab3ss 3395 resres 4890 inres 4895 imainrect 5043 restco 12721 restopnb 12728 |
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