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Mirrors > Home > ILE Home > Th. List > inrab2 | Unicode version |
Description: Intersection with a restricted class abstraction. (Contributed by NM, 19-Nov-2007.) |
Ref | Expression |
---|---|
inrab2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rab 2362 |
. . 3
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2 | abid2 2203 |
. . . 4
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3 | 2 | eqcomi 2087 |
. . 3
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4 | 1, 3 | ineq12i 3181 |
. 2
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5 | df-rab 2362 |
. . 3
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6 | inab 3248 |
. . . 4
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7 | elin 3165 |
. . . . . . 7
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8 | 7 | anbi1i 446 |
. . . . . 6
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9 | an32 527 |
. . . . . 6
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10 | 8, 9 | bitri 182 |
. . . . 5
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11 | 10 | abbii 2198 |
. . . 4
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12 | 6, 11 | eqtr4i 2106 |
. . 3
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13 | 5, 12 | eqtr4i 2106 |
. 2
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14 | 4, 13 | eqtr4i 2106 |
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 104 ax-ia2 105 ax-ia3 106 ax-io 663 ax-5 1377 ax-7 1378 ax-gen 1379 ax-ie1 1423 ax-ie2 1424 ax-8 1436 ax-10 1437 ax-11 1438 ax-i12 1439 ax-bndl 1440 ax-4 1441 ax-17 1460 ax-i9 1464 ax-ial 1468 ax-i5r 1469 ax-ext 2065 |
This theorem depends on definitions: df-bi 115 df-tru 1288 df-nf 1391 df-sb 1688 df-clab 2070 df-cleq 2076 df-clel 2079 df-nfc 2212 df-rab 2362 df-v 2612 df-in 2988 |
This theorem is referenced by: iooval2 9066 fzval2 9160 dfphi2 10803 znnen 10818 |
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