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Theorem hbsb 1823
 Description: If is not free in , it is not free in when and are distinct. (Contributed by NM, 12-Aug-1993.) (Proof rewritten by Jim Kingdon, 22-Mar-2018.)
Hypothesis
Ref Expression
hbsb.1
Assertion
Ref Expression
hbsb
Distinct variable group:   ,
Allowed substitution hints:   (,,)

Proof of Theorem hbsb
StepHypRef Expression
1 hbsb.1 . . . 4
21nfi 1351 . . 3
32nfsb 1822 . 2
43nfri 1412 1
 Colors of variables: wff set class Syntax hints:   wi 4  wal 1241  wsb 1645 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 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646 This theorem is referenced by:  sb10f  1871  hbsb4  1888  sb8euh  1923  hbab  2031  hblem  2145
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