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Theorem cbvralv2 3301
 Description: Rule used to change the bound variable in a restricted universal 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
cbvralv2
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hints:   ()   ()   ()   ()

Proof of Theorem cbvralv2
StepHypRef Expression
1 nfcv 2578 . 2
2 nfcv 2578 . 2
3 nfv 1630 . 2
4 nfv 1630 . 2
5 cbvralv2.2 . 2
6 cbvralv2.1 . 2
71, 2, 3, 4, 5, 6cbvralcsf 3297 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wceq 1653  wral 2711 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 1668  ax-8 1689  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953  ax-ext 2423 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 2429  df-cleq 2435  df-clel 2438  df-nfc 2567  df-ral 2716  df-sbc 3168  df-csb 3268
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