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Mirrors > Home > NFE 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 630 |
. . . 4
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2 | elin 3219 |
. . . . 5
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3 | 2 | anbi2i 675 |
. . . 4
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4 | 1, 3 | bitr4i 243 |
. . 3
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5 | elin 3219 |
. . . 4
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6 | 5 | anbi1i 676 |
. . 3
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7 | elin 3219 |
. . 3
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8 | 4, 6, 7 | 3bitr4i 268 |
. 2
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9 | 8 | ineqri 3449 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-v 2861 df-nin 3211 df-compl 3212 df-in 3213 |
This theorem is referenced by: in12 3466 in32 3467 in4 3471 indif2 3498 difun1 3514 dfrab3ss 3533 dfif4 3673 ssfin 4470 resres 4980 inres 4985 |
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