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Mirrors > Home > ILE Home > Th. List > rabxfrd | Unicode version |
Description: Class builder membership after substituting an expression (containing ) for in the class expression . (Contributed by NM, 16-Jan-2012.) |
Ref | Expression |
---|---|
rabxfrd.1 | |
rabxfrd.2 | |
rabxfrd.3 | |
rabxfrd.4 | |
rabxfrd.5 |
Ref | Expression |
---|---|
rabxfrd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rabxfrd.3 | . . . . . . . . . . 11 | |
2 | 1 | ex 113 | . . . . . . . . . 10 |
3 | ibibr 244 | . . . . . . . . . 10 | |
4 | 2, 3 | sylib 120 | . . . . . . . . 9 |
5 | 4 | imp 122 | . . . . . . . 8 |
6 | 5 | anbi1d 452 | . . . . . . 7 |
7 | rabxfrd.4 | . . . . . . . 8 | |
8 | 7 | elrab 2749 | . . . . . . 7 |
9 | rabid 2529 | . . . . . . 7 | |
10 | 6, 8, 9 | 3bitr4g 221 | . . . . . 6 |
11 | 10 | rabbidva 2592 | . . . . 5 |
12 | 11 | eleq2d 2148 | . . . 4 |
13 | rabxfrd.1 | . . . . 5 | |
14 | nfcv 2219 | . . . . 5 | |
15 | rabxfrd.2 | . . . . . 6 | |
16 | 15 | nfel1 2229 | . . . . 5 |
17 | rabxfrd.5 | . . . . . 6 | |
18 | 17 | eleq1d 2147 | . . . . 5 |
19 | 13, 14, 16, 18 | elrabf 2747 | . . . 4 |
20 | nfrab1 2533 | . . . . . 6 | |
21 | 13, 20 | nfel 2227 | . . . . 5 |
22 | eleq1 2141 | . . . . 5 | |
23 | 13, 14, 21, 22 | elrabf 2747 | . . . 4 |
24 | 12, 19, 23 | 3bitr3g 220 | . . 3 |
25 | pm5.32 440 | . . 3 | |
26 | 24, 25 | sylibr 132 | . 2 |
27 | 26 | imp 122 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 wceq 1284 wcel 1433 wnfc 2206 crab 2352 |
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 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-rab 2357 df-v 2603 |
This theorem is referenced by: rabxfr 4220 |
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