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Theorem bdsepnf 13116
 Description: Version of ax-bdsep 13112 with one disjoint variable condition removed, the other disjoint variable condition replaced by a non-freeness hypothesis, and without initial universal quantifier. See also bdsepnfALT 13117. Use bdsep1 13113 when sufficient. (Contributed by BJ, 5-Oct-2019.)
Hypotheses
Ref Expression
bdsepnf.nf
bdsepnf.1 BOUNDED
Assertion
Ref Expression
bdsepnf
Distinct variable group:   ,,
Allowed substitution hints:   (,,)

Proof of Theorem bdsepnf
StepHypRef Expression
1 bdsepnf.1 . . 3 BOUNDED
21bdsepnft 13115 . 2
3 bdsepnf.nf . 2
42, 3mpg 1427 1
 Colors of variables: wff set class Syntax hints:   wa 103   wb 104  wal 1329  wnf 1436  wex 1468  BOUNDED wbd 13040 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-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-4 1487  ax-14 1492  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121  ax-bdsep 13112 This theorem depends on definitions:  df-bi 116  df-nf 1437  df-cleq 2132  df-clel 2135 This theorem is referenced by: (None)
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