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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 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfa1 1521 | . . 3 | |
2 | nfv 1508 | . . . . . 6 | |
3 | nfnf1 1523 | . . . . . . 7 | |
4 | 3 | nfal 1555 | . . . . . 6 |
5 | nfsbt 1949 | . . . . . 6 | |
6 | nfv 1508 | . . . . . . 7 | |
7 | 6 | a1i 9 | . . . . . 6 |
8 | sbequ 1812 | . . . . . . 7 | |
9 | 8 | a1i 9 | . . . . . 6 |
10 | 2, 4, 5, 7, 9 | cbvrald 12995 | . . . . 5 |
11 | 10 | biimpd 143 | . . . 4 |
12 | 11 | imim1d 75 | . . 3 |
13 | 1, 12 | alimd 1501 | . 2 |
14 | ax-setind 4452 | . 2 | |
15 | 13, 14 | syl6 33 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wal 1329 wnf 1436 wsb 1735 wral 2416 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-setind 4452 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-sb 1736 df-cleq 2132 df-clel 2135 df-ral 2421 |
This theorem is referenced by: setindf 13164 |
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