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Mirrors > Home > ILE Home > Th. List > Mathboxes > setindft | Unicode version |
Description: Axiom of set-induction with a disjoint variable condition replaced with a non-freeness hypothesis (Contributed by BJ, 22-Nov-2019.) |
Ref | Expression |
---|---|
setindft |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfa1 1522 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | nfv 1509 |
. . . . . 6
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3 | nfnf1 1524 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() | |
4 | 3 | nfal 1556 |
. . . . . 6
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5 | nfsbt 1950 |
. . . . . 6
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6 | nfv 1509 |
. . . . . . 7
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7 | 6 | a1i 9 |
. . . . . 6
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8 | sbequ 1813 |
. . . . . . 7
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9 | 8 | a1i 9 |
. . . . . 6
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10 | 2, 4, 5, 7, 9 | cbvrald 13166 |
. . . . 5
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11 | 10 | biimpd 143 |
. . . 4
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12 | 11 | imim1d 75 |
. . 3
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13 | 1, 12 | alimd 1502 |
. 2
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14 | ax-setind 4460 |
. 2
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15 | 13, 14 | syl6 33 |
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-nf 1438 df-sb 1737 df-cleq 2133 df-clel 2136 df-ral 2422 |
This theorem is referenced by: setindf 13335 |
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