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Theorem cbvral2 28038
 Description: Change bound variables of double restricted universal quantification, using implicit substitution, analogous to cbvral2v 2949. (Contributed by Alexander van der Vekens, 2-Jul-2017.)
Hypotheses
Ref Expression
cbvral2.1
cbvral2.2
cbvral2.3
cbvral2.4
cbvral2.5
cbvral2.6
Assertion
Ref Expression
cbvral2
Distinct variable groups:   ,   ,   ,,   ,,   ,
Allowed substitution hints:   (,,,)   (,,,)   (,,,)   (,)

Proof of Theorem cbvral2
StepHypRef Expression
1 nfcv 2579 . . . 4
2 cbvral2.1 . . . 4
31, 2nfral 2766 . . 3
4 nfcv 2579 . . . 4
5 cbvral2.2 . . . 4
64, 5nfral 2766 . . 3
7 cbvral2.5 . . . 4
87ralbidv 2732 . . 3
93, 6, 8cbvral 2937 . 2
10 cbvral2.3 . . . 4
11 cbvral2.4 . . . 4
12 cbvral2.6 . . . 4
1310, 11, 12cbvral 2937 . . 3
1413ralbii 2736 . 2
159, 14bitri 242 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178  wnf 1554  wral 2712 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 1628  ax-9 1669  ax-8 1690  ax-6 1747  ax-7 1752  ax-11 1764  ax-12 1954  ax-ext 2424 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1661  df-cleq 2436  df-clel 2439  df-nfc 2568  df-ral 2717
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