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Theorem cbvrexv2 3318
 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:   ,   ,   ,   ,
Allowed substitution hints:   ()   ()   ()   ()

Proof of Theorem cbvrexv2
StepHypRef Expression
1 nfcv 2574 . 2
2 nfcv 2574 . 2
3 nfv 1630 . 2
4 nfv 1630 . 2
5 cbvralv2.2 . 2
6 cbvralv2.1 . 2
71, 2, 3, 4, 5, 6cbvrexcsf 3314 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wceq 1653  wrex 2708 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-rex 2713  df-sbc 3164  df-csb 3254
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