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Theorem ralab2 2705
 Description: Universal quantification over a class abstraction. (Contributed by Mario Carneiro, 3-Sep-2015.)
Hypothesis
Ref Expression
ralab2.1
Assertion
Ref Expression
ralab2
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem ralab2
StepHypRef Expression
1 df-ral 2311 . 2
2 nfsab1 2030 . . . 4
3 nfv 1421 . . . 4
42, 3nfim 1464 . . 3
5 nfv 1421 . . 3
6 eleq1 2100 . . . . 5
7 abid 2028 . . . . 5
86, 7syl6bb 185 . . . 4
9 ralab2.1 . . . 4
108, 9imbi12d 223 . . 3
114, 5, 10cbval 1637 . 2
121, 11bitri 173 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 98  wal 1241   wcel 1393  cab 2026  wral 2306 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-11 1397  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-ral 2311 This theorem is referenced by:  ralrab2  2706  ssintab  3632
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