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Theorem setindft 13247
 Description: Axiom of set-induction with a disjoint variable condition replaced with a non-freeness hypothesis (Contributed by BJ, 22-Nov-2019.)
Assertion
Ref Expression
setindft
Distinct variable group:   ,
Allowed substitution hints:   (,)

Proof of Theorem setindft
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 nfa1 1521 . . 3
2 nfv 1508 . . . . . 6
3 nfnf1 1523 . . . . . . 7
43nfal 1555 . . . . . 6
5 nfsbt 1949 . . . . . 6
6 nfv 1508 . . . . . . 7
76a1i 9 . . . . . 6
8 sbequ 1812 . . . . . . 7
98a1i 9 . . . . . 6
102, 4, 5, 7, 9cbvrald 13079 . . . . 5
1110biimpd 143 . . . 4
1211imim1d 75 . . 3
131, 12alimd 1501 . 2
14 ax-setind 4452 . 2
1513, 14syl6 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  13248
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