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Theorem gencbval 3155
 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:   ,   ,   ,   ,   ,

Proof of Theorem gencbval
StepHypRef Expression
1 gencbval.1 . . . 4
2 gencbval.2 . . . . 5
32notbid 294 . . . 4
4 gencbval.3 . . . 4
5 gencbval.4 . . . 4
61, 3, 4, 5gencbvex 3153 . . 3
7 exanali 1670 . . 3
8 exanali 1670 . . 3
96, 7, 83bitr3i 275 . 2
109con4bii 297 1
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  =wceq 1395  E.wex 1612  e.wcel 1818   cvv 3109 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-v 3111
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