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Theorem bdsep2 10393
 Description: Version of ax-bdsep 10391 with one DV condition removed and without initial universal quantifier. Use bdsep1 10392 when sufficient. (Contributed by BJ, 5-Oct-2019.)
Hypothesis
Ref Expression
bdsep2.1 BOUNDED
Assertion
Ref Expression
bdsep2
Distinct variable groups:   ,,   ,
Allowed substitution hints:   (,)

Proof of Theorem bdsep2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eleq2 2117 . . . . . 6
21anbi1d 446 . . . . 5
32bibi2d 225 . . . 4
43albidv 1721 . . 3
54exbidv 1722 . 2
6 bdsep2.1 . . 3 BOUNDED
76bdsep1 10392 . 2
85, 7chvarv 1828 1
 Colors of variables: wff set class Syntax hints:   wa 101   wb 102  wal 1257  wex 1397  BOUNDED wbd 10319 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-ext 2038  ax-bdsep 10391 This theorem depends on definitions:  df-bi 114  df-nf 1366  df-cleq 2049  df-clel 2052 This theorem is referenced by:  bdsepnft  10394  bdsepnfALT  10396
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