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Theorem cbvraldva2 3088
 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 461 . . . . 5
2 cbvraldva2.2 . . . . 5
31, 2eleq12d 2539 . . . 4
4 cbvraldva2.1 . . . 4
53, 4imbi12d 320 . . 3
65cbvaldva 2033 . 2
7 df-ral 2812 . 2
8 df-ral 2812 . 2
96, 7, 83bitr4g 288 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369  wal 1393   wceq 1395   wcel 1819  wral 2807 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-10 1838  ax-11 1843  ax-12 1855  ax-13 2000  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1614  df-nf 1618  df-cleq 2449  df-clel 2452  df-ral 2812 This theorem is referenced by:  cbvraldva  3090  tfrlem3a  7064  mreexexlemd  15061
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