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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 2477 |
. . 3
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2 | abid2 2310 |
. . . 4
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3 | 2 | eqcomi 2193 |
. . 3
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4 | 1, 3 | ineq12i 3349 |
. 2
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5 | df-rab 2477 |
. . 3
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6 | inab 3418 |
. . . 4
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7 | elin 3333 |
. . . . . . 7
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8 | 7 | anbi1i 458 |
. . . . . 6
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9 | an32 562 |
. . . . . 6
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10 | 8, 9 | bitri 184 |
. . . . 5
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11 | 10 | abbii 2305 |
. . . 4
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12 | 6, 11 | eqtr4i 2213 |
. . 3
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13 | 5, 12 | eqtr4i 2213 |
. 2
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14 | 4, 13 | eqtr4i 2213 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-rab 2477 df-v 2754 df-in 3150 |
This theorem is referenced by: iooval2 9947 fzval2 10043 dfphi2 12255 znnen 12452 |
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