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Theorem cbvrexv2 2913
 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 2178 . 2
2 nfcv 2178 . 2
3 nfv 1421 . 2
4 nfv 1421 . 2
5 cbvralv2.2 . 2
6 cbvralv2.1 . 2
71, 2, 3, 4, 5, 6cbvrexcsf 2909 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 98   wceq 1243  wrex 2307 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-rex 2312  df-sbc 2765  df-csb 2853 This theorem is referenced by: (None)
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