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Mirrors > Home > ILE Home > Th. List > inrab | Unicode version |
Description: Intersection of two restricted class abstractions. (Contributed by NM, 1-Sep-2006.) |
Ref | Expression |
---|---|
inrab |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rab 2423 | . . 3 | |
2 | df-rab 2423 | . . 3 | |
3 | 1, 2 | ineq12i 3270 | . 2 |
4 | df-rab 2423 | . . 3 | |
5 | inab 3339 | . . . 4 | |
6 | anandi 579 | . . . . 5 | |
7 | 6 | abbii 2253 | . . . 4 |
8 | 5, 7 | eqtr4i 2161 | . . 3 |
9 | 4, 8 | eqtr4i 2161 | . 2 |
10 | 3, 9 | eqtr4i 2161 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wceq 1331 wcel 1480 cab 2123 crab 2418 cin 3065 |
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 2119 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-rab 2423 df-v 2683 df-in 3072 |
This theorem is referenced by: rabnc 3390 iooinsup 11039 phiprmpw 11887 unennn 11899 |
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