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Theorem cbvrexdva2 2937
 Description: Rule used to change the bound variable in a restricted existential 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
cbvrexdva2
Distinct variable groups:   ,   ,   ,   ,   ,,
Allowed substitution hints:   ()   ()   ()   ()

Proof of Theorem cbvrexdva2
StepHypRef Expression
1 simpr 448 . . . . 5
2 cbvraldva2.2 . . . . 5
31, 2eleq12d 2504 . . . 4
4 cbvraldva2.1 . . . 4
53, 4anbi12d 692 . . 3
65cbvexdva 1995 . 2
7 df-rex 2711 . 2
8 df-rex 2711 . 2
96, 7, 83bitr4g 280 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wex 1550   wceq 1652   wcel 1725  wrex 2706 This theorem is referenced by:  cbvrexdva  2939  mreexexlemd  13869 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-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-nf 1554  df-cleq 2429  df-clel 2432  df-rex 2711
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