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Theorem ralab2 3203
 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 2742 . 2
2 nfsab1 2441 . . . 4
3 nfv 1761 . . . 4
42, 3nfim 2003 . . 3
5 nfv 1761 . . 3
6 eleq1 2517 . . . . 5
7 abid 2439 . . . . 5
86, 7syl6bb 265 . . . 4
9 ralab2.1 . . . 4
108, 9imbi12d 322 . . 3
114, 5, 10cbval 2114 . 2
121, 11bitri 253 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 188  wal 1442   wcel 1887  cab 2437  wral 2737 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851  ax-10 1915  ax-11 1920  ax-12 1933  ax-13 2091  ax-ext 2431 This theorem depends on definitions:  df-bi 189  df-an 373  df-ex 1664  df-nf 1668  df-sb 1798  df-clab 2438  df-cleq 2444  df-clel 2447  df-ral 2742 This theorem is referenced by:  ralrab2  3204  ssintab  4251  efgval  17367  efger  17368  elintabg  36180  elintima  36245
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