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Mirrors > Home > ILE Home > Th. List > elrabf | Unicode version |
Description: Membership in a restricted class abstraction, using implicit substitution. This version has bound-variable hypotheses in place of distinct variable restrictions. (Contributed by NM, 21-Sep-2003.) |
Ref | Expression |
---|---|
elrabf.1 |
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elrabf.2 |
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elrabf.3 |
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elrabf.4 |
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Ref | Expression |
---|---|
elrabf |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 2763 |
. 2
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2 | elex 2763 |
. . 3
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3 | 2 | adantr 276 |
. 2
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4 | df-rab 2477 |
. . . 4
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5 | 4 | eleq2i 2256 |
. . 3
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6 | elrabf.1 |
. . . 4
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7 | elrabf.2 |
. . . . . 6
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8 | 6, 7 | nfel 2341 |
. . . . 5
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9 | elrabf.3 |
. . . . 5
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10 | 8, 9 | nfan 1576 |
. . . 4
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11 | eleq1 2252 |
. . . . 5
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12 | elrabf.4 |
. . . . 5
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13 | 11, 12 | anbi12d 473 |
. . . 4
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14 | 6, 10, 13 | elabgf 2894 |
. . 3
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15 | 5, 14 | bitrid 192 |
. 2
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16 | 1, 3, 15 | pm5.21nii 705 |
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-rab 2477 df-v 2754 |
This theorem is referenced by: elrab 2908 frind 4370 rabxfrd 4487 infssuzcldc 11987 nnwosdc 12075 |
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