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Theorem bdsepnfALT 10009
 Description: Alternate proof of bdsepnf 10008, not using bdsepnft 10007. (Contributed by BJ, 5-Oct-2019.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
bdsepnf.nf
bdsepnf.1 BOUNDED
Assertion
Ref Expression
bdsepnfALT
Distinct variable group:   ,,
Allowed substitution hints:   (,,)

Proof of Theorem bdsepnfALT
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 bdsepnf.1 . . 3 BOUNDED
21bdsep2 10006 . 2
3 nfv 1421 . . . . 5
4 nfv 1421 . . . . . 6
5 bdsepnf.nf . . . . . 6
64, 5nfan 1457 . . . . 5
73, 6nfbi 1481 . . . 4
87nfal 1468 . . 3
9 nfv 1421 . . 3
10 elequ2 1601 . . . . 5
1110bibi1d 222 . . . 4
1211albidv 1705 . . 3
138, 9, 12cbvex 1639 . 2
142, 13mpbi 133 1
 Colors of variables: wff set class Syntax hints:   wa 97   wb 98  wal 1241  wnf 1349  wex 1381  BOUNDED wbd 9932 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 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-4 1400  ax-14 1405  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-bdsep 10004 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-cleq 2033  df-clel 2036 This theorem is referenced by: (None)
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