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Theorem cbvrex2 27918
 Description: Change bound variables of double restricted universal quantification, using implicit substitution, analogous to cbvrex2v 2933. (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
cbvrex2
Distinct variable groups:   ,   ,   ,,   ,,   ,
Allowed substitution hints:   (,,,)   (,,,)   (,,,)   (,)

Proof of Theorem cbvrex2
StepHypRef Expression
1 nfcv 2571 . . . 4
2 cbvral2.1 . . . 4
31, 2nfrex 2753 . . 3
4 nfcv 2571 . . . 4
5 cbvral2.2 . . . 4
64, 5nfrex 2753 . . 3
7 cbvral2.5 . . . 4
87rexbidv 2718 . . 3
93, 6, 8cbvrex 2921 . 2
10 cbvral2.3 . . . 4
11 cbvral2.4 . . . 4
12 cbvral2.6 . . . 4
1310, 11, 12cbvrex 2921 . . 3
1413rexbii 2722 . 2
159, 14bitri 241 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177  wnf 1553  wrex 2698 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-rex 2703
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