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Theorem cbvrexv2 3203
 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 2489 . 2
2 nfcv 2489 . 2
3 nfv 1619 . 2
4 nfv 1619 . 2
5 cbvralv2.2 . 2
6 cbvralv2.1 . 2
71, 2, 3, 4, 5, 6cbvrexcsf 3199 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wceq 1642  wrex 2615 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ral 2619  df-rex 2620  df-sbc 3047  df-csb 3137 This theorem is referenced by: (None)
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