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Theorem setindft 9425
Description: Axiom of set-induction with a DV condition replaced with a non-freeness hypothesis (Contributed by BJ, 22-Nov-2019.)
Assertion
Ref Expression
setindft  F/
Distinct variable group:   ,
Allowed substitution hints:   (,)

Proof of Theorem setindft
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 nfa1 1431 . . 3  F/ F/
2 nfv 1418 . . . . . 6  F/ F/
3 nfnf1 1433 . . . . . . 7  F/ F/
43nfal 1465 . . . . . 6  F/ F/
5 nfsbt 1847 . . . . . 6  F/  F/
6 nfv 1418 . . . . . . 7  F/
76a1i 9 . . . . . 6  F/  F/
8 sbequ 1718 . . . . . . 7
98a1i 9 . . . . . 6  F/
102, 4, 5, 7, 9cbvrald 9262 . . . . 5  F/
1110biimpd 132 . . . 4  F/
1211imim1d 69 . . 3  F/
131, 12alimd 1411 . 2  F/
14 ax-setind 4220 . 2
1513, 14syl6 29 1  F/
Colors of variables: wff set class
Syntax hints:   wi 4   wb 98  wal 1240   F/wnf 1346  wsb 1642  wral 2300
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019  ax-setind 4220
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-cleq 2030  df-clel 2033  df-ral 2305
This theorem is referenced by:  setindf  9426
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