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Theorem ralm 3319
Description: Inhabited classes and restricted quantification. (Contributed by Jim Kingdon, 6-Aug-2018.)
Assertion
Ref Expression
ralm

Proof of Theorem ralm
StepHypRef Expression
1 df-ral 2305 . . . . . 6
21imbi2i 215 . . . . 5
3 19.38 1563 . . . . 5
42, 3sylbi 114 . . . 4
5 pm2.43 47 . . . . 5
65alimi 1341 . . . 4
74, 6syl 14 . . 3
87, 1sylibr 137 . 2
9 ax-1 5 . 2
108, 9impbii 117 1
Colors of variables: wff set class
Syntax hints:   wi 4   wb 98  wal 1240  wex 1378   wcel 1390  wral 2300
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-ial 1424  ax-i5r 1425
This theorem depends on definitions:  df-bi 110  df-ral 2305
This theorem is referenced by:  raaan  3321
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