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Mirrors > Home > ILE Home > Th. List > elrabd | Unicode version |
Description: Membership in a restricted class abstraction, using implicit substitution. Deduction version of elrab 2868. (Contributed by Glauco Siliprandi, 23-Oct-2021.) |
Ref | Expression |
---|---|
elrabd.1 | |
elrabd.2 | |
elrabd.3 |
Ref | Expression |
---|---|
elrabd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elrabd.2 | . . 3 | |
2 | elrabd.3 | . . 3 | |
3 | 1, 2 | jca 304 | . 2 |
4 | elrabd.1 | . . 3 | |
5 | 4 | elrab 2868 | . 2 |
6 | 3, 5 | sylibr 133 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1335 wcel 2128 crab 2439 |
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 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-rab 2444 df-v 2714 |
This theorem is referenced by: ctssdccl 7050 suplocexprlemru 7634 suplocexprlemloc 7636 phisum 12107 znnen 12114 ennnfonelemj0 12117 ennnfonelemg 12119 cdivcncfap 12974 cnopnap 12981 ivthinc 13008 limcdifap 13018 limcimolemlt 13020 dvcoapbr 13058 subctctexmid 13560 |
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