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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 114 | . . . . . . . . . 10 |
3 | ibibr 245 | . . . . . . . . . 10 | |
4 | 2, 3 | sylib 121 | . . . . . . . . 9 |
5 | 4 | imp 123 | . . . . . . . 8 |
6 | 5 | anbi1d 462 | . . . . . . 7 |
7 | rabxfrd.4 | . . . . . . . 8 | |
8 | 7 | elrab 2886 | . . . . . . 7 |
9 | rabid 2645 | . . . . . . 7 | |
10 | 6, 8, 9 | 3bitr4g 222 | . . . . . 6 |
11 | 10 | rabbidva 2718 | . . . . 5 |
12 | 11 | eleq2d 2240 | . . . 4 |
13 | rabxfrd.1 | . . . . 5 | |
14 | nfcv 2312 | . . . . 5 | |
15 | rabxfrd.2 | . . . . . 6 | |
16 | 15 | nfel1 2323 | . . . . 5 |
17 | rabxfrd.5 | . . . . . 6 | |
18 | 17 | eleq1d 2239 | . . . . 5 |
19 | 13, 14, 16, 18 | elrabf 2884 | . . . 4 |
20 | nfrab1 2649 | . . . . . 6 | |
21 | 13, 20 | nfel 2321 | . . . . 5 |
22 | eleq1 2233 | . . . . 5 | |
23 | 13, 14, 21, 22 | elrabf 2884 | . . . 4 |
24 | 12, 19, 23 | 3bitr3g 221 | . . 3 |
25 | pm5.32 450 | . . 3 | |
26 | 24, 25 | sylibr 133 | . 2 |
27 | 26 | imp 123 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1348 wcel 2141 wnfc 2299 crab 2452 |
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-ral 2453 df-rab 2457 df-v 2732 |
This theorem is referenced by: rabxfr 4455 |
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