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Mirrors > Home > ILE Home > Th. List > setind | Unicode version |
Description: Set (epsilon) induction. Theorem 5.22 of [TakeutiZaring] p. 21. (Contributed by NM, 17-Sep-2003.) |
Ref | Expression |
---|---|
setind |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfss2 3091 |
. . . 4
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2 | 1 | imbi1i 237 |
. . 3
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3 | 2 | albii 1447 |
. 2
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4 | setindel 4461 |
. 2
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5 | 3, 4 | sylbi 120 |
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 ax-setind 4460 |
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-ral 2422 df-v 2691 df-in 3082 df-ss 3089 |
This theorem is referenced by: setind2 4463 |
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