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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 2457 | . . 3 | |
2 | df-rab 2457 | . . 3 | |
3 | 1, 2 | ineq12i 3326 | . 2 |
4 | df-rab 2457 | . . 3 | |
5 | inab 3395 | . . . 4 | |
6 | anandi 585 | . . . . 5 | |
7 | 6 | abbii 2286 | . . . 4 |
8 | 5, 7 | eqtr4i 2194 | . . 3 |
9 | 4, 8 | eqtr4i 2194 | . 2 |
10 | 3, 9 | eqtr4i 2194 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wceq 1348 wcel 2141 cab 2156 crab 2452 cin 3120 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-rab 2457 df-v 2732 df-in 3127 |
This theorem is referenced by: rabnc 3446 iooinsup 11227 phiprmpw 12163 unennn 12339 |
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