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Theorem bdsep2 9341
Description: Version of ax-bdsep 9339 with one DV condition removed and without initial universal quantifier. Use bdsep1 9340 when sufficient. (Contributed by BJ, 5-Oct-2019.)
Hypothesis
Ref Expression
bdsep2.1 BOUNDED
Assertion
Ref Expression
bdsep2  b  b  a
Distinct variable groups:    a, b,   , b
Allowed substitution hints:   (, a)

Proof of Theorem bdsep2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eleq2 2098 . . . . . 6  a  a
21anbi1d 438 . . . . 5  a  a
32bibi2d 221 . . . 4  a  b  b  a
43albidv 1702 . . 3  a  b  b  a
54exbidv 1703 . 2  a  b  b  b  b  a
6 bdsep2.1 . . 3 BOUNDED
76bdsep1 9340 . 2  b  b
85, 7chvarv 1809 1  b  b  a
Colors of variables: wff set class
Syntax hints:   wa 97   wb 98  wal 1240  wex 1378  BOUNDED wbd 9267
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-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-ext 2019  ax-bdsep 9339
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-cleq 2030  df-clel 2033
This theorem is referenced by:  bdsepnft  9342  bdsepnfALT  9344
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