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Theorem gencbval 3094
 Description: Change of bound variable using implicit substitution. (Contributed by NM, 17-May-1996.)
Hypotheses
Ref Expression
gencbval.1
gencbval.2
gencbval.3
gencbval.4
Assertion
Ref Expression
gencbval
Distinct variable groups:   ,   ,   ,   ,   ,
Allowed substitution hints:   ()   ()   ()   ()   ()

Proof of Theorem gencbval
StepHypRef Expression
1 gencbval.1 . . . 4
2 gencbval.2 . . . . 5
32notbid 296 . . . 4
4 gencbval.3 . . . 4
5 gencbval.4 . . . 4
61, 3, 4, 5gencbvex 3092 . . 3
7 exanali 1721 . . 3
8 exanali 1721 . . 3
96, 7, 83bitr3i 279 . 2
109con4bii 299 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 188   wa 371  wal 1442   wceq 1444  wex 1663   wcel 1887  cvv 3045 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-ext 2431 This theorem depends on definitions:  df-bi 189  df-an 373  df-tru 1447  df-ex 1664  df-nf 1668  df-sb 1798  df-clab 2438  df-cleq 2444  df-clel 2447  df-v 3047 This theorem is referenced by: (None)
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