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Theorem cbvrexv2 3471
Description: Rule used to change the bound variable in a restricted existential quantifier with implicit substitution which also changes the quantifier domain. (Contributed by David Moews, 1-May-2017.)
Hypotheses
Ref Expression
cbvralv2.1
cbvralv2.2
Assertion
Ref Expression
cbvrexv2
Distinct variable groups:   ,   ,   ,   ,

Proof of Theorem cbvrexv2
StepHypRef Expression
1 nfcv 2619 . 2
2 nfcv 2619 . 2
3 nfv 1707 . 2
4 nfv 1707 . 2
5 cbvralv2.2 . 2
6 cbvralv2.1 . 2
71, 2, 3, 4, 5, 6cbvrexcsf 3467 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  =wceq 1395  E.wrex 2808
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-sbc 3328  df-csb 3435
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