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Theorem bdzfauscl 13403
 Description: Closed form of the version of zfauscl 4080 for bounded formulas using bounded separation. (Contributed by BJ, 13-Nov-2019.)
Hypothesis
Ref Expression
bdzfauscl.bd BOUNDED
Assertion
Ref Expression
bdzfauscl
Distinct variable groups:   ,,   ,
Allowed substitution hints:   ()   (,)

Proof of Theorem bdzfauscl
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eleq2 2218 . . . . . 6
21anbi1d 461 . . . . 5
32bibi2d 231 . . . 4
43albidv 1801 . . 3
54exbidv 1802 . 2
6 bdzfauscl.bd . . 3 BOUNDED
76bdsep1 13398 . 2
85, 7vtoclg 2769 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104  wal 1330   wceq 1332  wex 1469   wcel 2125  BOUNDED wbd 13325 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-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-10 1482  ax-11 1483  ax-i12 1484  ax-bndl 1486  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-ext 2136  ax-bdsep 13397 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1740  df-clab 2141  df-cleq 2147  df-clel 2150  df-nfc 2285  df-v 2711 This theorem is referenced by:  bdinex1  13412
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