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Mirrors > Home > ILE Home > Th. List > elab2 | Unicode version |
Description: Membership in a class abstraction, using implicit substitution. (Contributed by NM, 13-Sep-1995.) |
Ref | Expression |
---|---|
elab2.1 |
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elab2.2 |
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elab2.3 |
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Ref | Expression |
---|---|
elab2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elab2.1 |
. 2
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2 | elab2.2 |
. . 3
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3 | elab2.3 |
. . 3
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4 | 2, 3 | elab2g 2784 |
. 2
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5 | 1, 4 | ax-mp 7 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 671 ax-5 1391 ax-7 1392 ax-gen 1393 ax-ie1 1437 ax-ie2 1438 ax-8 1450 ax-10 1451 ax-11 1452 ax-i12 1453 ax-bndl 1454 ax-4 1455 ax-17 1474 ax-i9 1478 ax-ial 1482 ax-i5r 1483 ax-ext 2082 |
This theorem depends on definitions: df-bi 116 df-tru 1302 df-nf 1405 df-sb 1704 df-clab 2087 df-cleq 2093 df-clel 2096 df-nfc 2229 df-v 2643 |
This theorem is referenced by: elpw 3463 elint 3724 opabid 4117 elrn2 4719 elimasn 4842 oprabid 5735 tfrlem3a 6137 tfrcllemsucaccv 6181 tfrcllembxssdm 6183 tfrcllemres 6189 addnqprlemrl 7266 addnqprlemru 7267 addnqprlemfl 7268 addnqprlemfu 7269 mulnqprlemrl 7282 mulnqprlemru 7283 mulnqprlemfl 7284 mulnqprlemfu 7285 ltnqpr 7302 ltnqpri 7303 archpr 7352 cauappcvgprlemladdfu 7363 cauappcvgprlemladdfl 7364 caucvgprlemladdfu 7386 caucvgprprlemopu 7408 txuni2 12206 |
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