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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 2894. (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 306 |
. 2
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4 | elrabd.1 |
. . 3
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5 | 4 | elrab 2894 |
. 2
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6 | 3, 5 | sylibr 134 |
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 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-rab 2464 df-v 2740 |
This theorem is referenced by: ctssdccl 7110 suplocexprlemru 7718 suplocexprlemloc 7720 zsupssdc 11955 uzwodc 12038 phisum 12240 odzcllem 12242 pcpremul 12293 znnen 12399 ennnfonelemj0 12402 ennnfonelemg 12404 issubmd 12865 mhmeql 12876 cdivcncfap 14090 cnopnap 14097 ivthinc 14124 limcdifap 14134 limcimolemlt 14136 dvcoapbr 14174 subctctexmid 14753 |
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