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Theorem setindf 13333
 Description: Axiom of set-induction with a disjoint variable condition replaced with a non-freeness hypothesis (Contributed by BJ, 22-Nov-2019.)
Hypothesis
Ref Expression
setindf.nf
Assertion
Ref Expression
setindf
Distinct variable group:   ,
Allowed substitution hints:   (,)

Proof of Theorem setindf
StepHypRef Expression
1 setindft 13332 . 2
2 setindf.nf . 2
31, 2mpg 1428 1
 Colors of variables: wff set class Syntax hints:   wi 4  wal 1330  wnf 1437  wsb 1736  wral 2417 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 4459 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: (None)
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