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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 2844. (Contributed by Glauco Siliprandi, 23-Oct-2021.) |
Ref | Expression |
---|---|
elrabd.1 |
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elrabd.2 |
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elrabd.3 |
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Ref | Expression |
---|---|
elrabd |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elrabd.2 |
. . 3
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2 | elrabd.3 |
. . 3
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3 | 1, 2 | jca 304 |
. 2
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4 | elrabd.1 |
. . 3
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5 | 4 | elrab 2844 |
. 2
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6 | 3, 5 | sylibr 133 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
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 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-rab 2426 df-v 2691 |
This theorem is referenced by: ctssdccl 7004 suplocexprlemru 7551 suplocexprlemloc 7553 znnen 11947 ennnfonelemj0 11950 ennnfonelemg 11952 cdivcncfap 12795 cnopnap 12802 ivthinc 12829 limcdifap 12839 limcimolemlt 12841 dvcoapbr 12879 subctctexmid 13369 |
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