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Mirrors > Home > ILE Home > Th. List > elabgf | Unicode version |
Description: Membership in a class abstraction, using implicit substitution. Compare Theorem 6.13 of [Quine] p. 44. This version has bound-variable hypotheses in place of distinct variable restrictions. (Contributed by NM, 21-Sep-2003.) (Revised by Mario Carneiro, 12-Oct-2016.) |
Ref | Expression |
---|---|
elabgf.1 |
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elabgf.2 |
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elabgf.3 |
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Ref | Expression |
---|---|
elabgf |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elabgf.1 |
. 2
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2 | nfab1 2284 |
. . . 4
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3 | 1, 2 | nfel 2291 |
. . 3
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4 | elabgf.2 |
. . 3
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5 | 3, 4 | nfbi 1569 |
. 2
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6 | eleq1 2203 |
. . 3
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7 | elabgf.3 |
. . 3
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8 | 6, 7 | bibi12d 234 |
. 2
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9 | abid 2128 |
. 2
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10 | 1, 5, 8, 9 | vtoclgf 2747 |
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-v 2691 |
This theorem is referenced by: elabf 2831 elabg 2834 elab3gf 2838 elrabf 2842 bj-intabssel 13167 |
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