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Theorem cbvraldva2 2839
 Description: Rule used to change the bound variable in a restricted universal quantifier with implicit substitution which also changes the quantifier domain. Deduction form. (Contributed by David Moews, 1-May-2017.)
Hypotheses
Ref Expression
cbvraldva2.1
cbvraldva2.2
Assertion
Ref Expression
cbvraldva2
Distinct variable groups:   ,   ,   ,   ,   ,,
Allowed substitution hints:   ()   ()   ()   ()

Proof of Theorem cbvraldva2
StepHypRef Expression
1 simpr 447 . . . . 5
2 cbvraldva2.2 . . . . 5
31, 2eleq12d 2421 . . . 4
4 cbvraldva2.1 . . . 4
53, 4imbi12d 311 . . 3
65cbvaldva 2010 . 2
7 df-ral 2619 . 2
8 df-ral 2619 . 2
96, 7, 83bitr4g 279 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358  wal 1540   wceq 1642   wcel 1710  wral 2614 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-cleq 2346  df-clel 2349  df-ral 2619 This theorem is referenced by:  cbvraldva  2841
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