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Theorem bdbm1.3ii 7309
Description: Bounded version of bm1.3ii 3848. (Contributed by BJ, 5-Oct-2019.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
bdbm1.3ii.bd BOUNDED
bdbm1.3ii.1
Assertion
Ref Expression
bdbm1.3ii
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem bdbm1.3ii
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 bdbm1.3ii.1 . . . . 5
2 elequ2 1579 . . . . . . . 8
32imbi2d 219 . . . . . . 7
43albidv 1683 . . . . . 6
54cbvexv 1773 . . . . 5
61, 5mpbi 133 . . . 4
7 bdbm1.3ii.bd . . . . 5 BOUNDED
87bdsep2 7304 . . . 4
96, 8pm3.2i 257 . . 3
109exan 1561 . 2
11 19.42v 1764 . . . 4
12 bimsc1 856 . . . . . 6
1312alanimi 1324 . . . . 5
1413eximi 1469 . . . 4
1511, 14sylbir 125 . . 3
1615exlimiv 1467 . 2
1710, 16ax-mp 7 1
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98  wal 1224  wex 1358  BOUNDED wbd 7231
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 1312  ax-7 1313  ax-gen 1314  ax-ie1 1359  ax-ie2 1360  ax-8 1372  ax-4 1377  ax-14 1382  ax-17 1396  ax-i9 1400  ax-ial 1405  ax-ext 2000  ax-bdsep 7303
This theorem depends on definitions:  df-bi 110  df-nf 1326  df-cleq 2011  df-clel 2014
This theorem is referenced by:  bj-zfpair2  7325  bj-axun2  7330  bj-uniex2  7331
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