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Theorem gencbval 2992
 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 286 . . . 4
4 gencbval.3 . . . 4
5 gencbval.4 . . . 4
61, 3, 4, 5gencbvex 2990 . . 3
7 exanali 1595 . . 3
8 exanali 1595 . . 3
96, 7, 83bitr3i 267 . 2
109con4bii 289 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 177   wa 359  wal 1549  wex 1550   wceq 1652   wcel 1725  cvv 2948 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-ext 2416 This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-v 2950
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