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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 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rab 2425 | . . 3 | |
2 | abid2 2260 | . . . 4 | |
3 | 2 | eqcomi 2143 | . . 3 |
4 | 1, 3 | ineq12i 3275 | . 2 |
5 | df-rab 2425 | . . 3 | |
6 | inab 3344 | . . . 4 | |
7 | elin 3259 | . . . . . . 7 | |
8 | 7 | anbi1i 453 | . . . . . 6 |
9 | an32 551 | . . . . . 6 | |
10 | 8, 9 | bitri 183 | . . . . 5 |
11 | 10 | abbii 2255 | . . . 4 |
12 | 6, 11 | eqtr4i 2163 | . . 3 |
13 | 5, 12 | eqtr4i 2163 | . 2 |
14 | 4, 13 | eqtr4i 2163 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wceq 1331 wcel 1480 cab 2125 crab 2420 cin 3070 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-rab 2425 df-v 2688 df-in 3077 |
This theorem is referenced by: iooval2 9698 fzval2 9793 dfphi2 11896 znnen 11911 |
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