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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 2899 |
. 2
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5 | 1, 4 | ax-mp 5 |
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 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-v 2754 |
This theorem is referenced by: elpw 3596 elint 3865 opabid 4275 elrn2 4887 elimasn 5013 oprabid 5928 tfrlem3a 6335 tfrcllemsucaccv 6379 tfrcllembxssdm 6381 tfrcllemres 6387 addnqprlemrl 7586 addnqprlemru 7587 addnqprlemfl 7588 addnqprlemfu 7589 mulnqprlemrl 7602 mulnqprlemru 7603 mulnqprlemfl 7604 mulnqprlemfu 7605 ltnqpr 7622 ltnqpri 7623 archpr 7672 cauappcvgprlemladdfu 7683 cauappcvgprlemladdfl 7684 caucvgprlemladdfu 7706 caucvgprprlemopu 7728 suplocexprlemloc 7750 4sqlem12 12434 txuni2 14216 |
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