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Mirrors > Home > ILE Home > Th. List > elab2g | Unicode version |
Description: Membership in a class abstraction, using implicit substitution. (Contributed by NM, 13-Sep-1995.) |
Ref | Expression |
---|---|
elab2g.1 |
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elab2g.2 |
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Ref | Expression |
---|---|
elab2g |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elab2g.2 |
. . 3
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2 | 1 | eleq2i 2101 |
. 2
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3 | elab2g.1 |
. . 3
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4 | 3 | elabg 2682 |
. 2
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5 | 2, 4 | syl5bb 181 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 629 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-10 1393 ax-11 1394 ax-i12 1395 ax-bndl 1396 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 |
This theorem depends on definitions: df-bi 110 df-tru 1245 df-nf 1347 df-sb 1643 df-clab 2024 df-cleq 2030 df-clel 2033 df-nfc 2164 df-v 2553 |
This theorem is referenced by: elab2 2684 elab4g 2685 eldif 2921 elun 3078 elin 3120 elprg 3384 elsncg 3389 eluni 3574 eliun 3652 eliin 3653 elopab 3986 elong 4076 opeliunxp 4338 elrn2g 4468 eldmg 4473 elrnmpt 4526 elrnmpt1 4528 elimag 4615 elrnmpt2g 5555 eloprabi 5764 tfrlem3ag 5865 elqsg 6092 1idprl 6566 1idpru 6567 recexprlemell 6594 recexprlemelu 6595 |
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