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Theorem ralrab 2846
 Description: Universal quantification over a restricted class abstraction. (Contributed by Jeff Madsen, 10-Jun-2010.)
Hypothesis
Ref Expression
ralab.1
Assertion
Ref Expression
ralrab
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   (,)   ()   (,)   ()

Proof of Theorem ralrab
StepHypRef Expression
1 ralab.1 . . . . 5
21elrab 2841 . . . 4
32imbi1i 237 . . 3
4 impexp 261 . . 3
53, 4bitri 183 . 2
65ralbii2 2446 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104   wcel 1481  wral 2417  crab 2421 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 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-ral 2422  df-rab 2426  df-v 2689 This theorem is referenced by:  limcdifap  12830
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