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Theorem gencbval 2903
 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 285 . . . 4
4 gencbval.3 . . . 4
5 gencbval.4 . . . 4
61, 3, 4, 5gencbvex 2901 . . 3
7 exanali 1585 . . 3
8 exanali 1585 . . 3
96, 7, 83bitr3i 266 . 2
109con4bii 288 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 176   wa 358  wal 1540  wex 1541   wceq 1642   wcel 1710  cvv 2859 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-v 2861 This theorem is referenced by: (None)
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