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Theorem ralab2 3264
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:   ,   ,   ,   ,

Proof of Theorem ralab2
StepHypRef Expression
1 df-ral 2812 . 2
2 nfsab1 2446 . . . 4
3 nfv 1707 . . . 4
42, 3nfim 1920 . . 3
5 nfv 1707 . . 3
6 eleq1 2529 . . . . 5
7 abid 2444 . . . . 5
86, 7syl6bb 261 . . . 4
9 ralab2.1 . . . 4
108, 9imbi12d 320 . . 3
114, 5, 10cbval 2021 . 2
121, 11bitri 249 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  A.wal 1393  e.wcel 1818  {cab 2442  A.wral 2807
This theorem is referenced by:  ralrab2  3265  ssintab  4303  efgval  16735  efger  16736  elintima  37765
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-ral 2812
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