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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 2368 |
. . 3
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2 | abid2 2208 |
. . . 4
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3 | 2 | eqcomi 2092 |
. . 3
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4 | 1, 3 | ineq12i 3199 |
. 2
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5 | df-rab 2368 |
. . 3
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6 | inab 3267 |
. . . 4
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7 | elin 3183 |
. . . . . . 7
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8 | 7 | anbi1i 446 |
. . . . . 6
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9 | an32 529 |
. . . . . 6
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10 | 8, 9 | bitri 182 |
. . . . 5
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11 | 10 | abbii 2203 |
. . . 4
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12 | 6, 11 | eqtr4i 2111 |
. . 3
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13 | 5, 12 | eqtr4i 2111 |
. 2
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14 | 4, 13 | eqtr4i 2111 |
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 665 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-10 1441 ax-11 1442 ax-i12 1443 ax-bndl 1444 ax-4 1445 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 |
This theorem depends on definitions: df-bi 115 df-tru 1292 df-nf 1395 df-sb 1693 df-clab 2075 df-cleq 2081 df-clel 2084 df-nfc 2217 df-rab 2368 df-v 2621 df-in 3005 |
This theorem is referenced by: iooval2 9323 fzval2 9417 dfphi2 11461 znnen 11476 |
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