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Theorem ralab2 3101
 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 2712 . 2
2 nfsab1 2428 . . . 4
3 nfv 1630 . . . 4
42, 3nfim 1833 . . 3
5 nfv 1630 . . 3
6 eleq1 2498 . . . . 5
7 abid 2426 . . . . 5
86, 7syl6bb 254 . . . 4
9 ralab2.1 . . . 4
108, 9imbi12d 313 . . 3
114, 5, 10cbval 1983 . 2
121, 11bitri 242 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178  wal 1550   wcel 1726  cab 2424  wral 2707 This theorem is referenced by:  ralrab2  3102  ssintab  4069  efgval  15354  efger  15355 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-ral 2712
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