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Theorem rexcom4f 28111
 Description: Commutation of restricted and unrestricted existential quantifiers. (Contributed by NM, 12-Apr-2004.) (Proof shortened by Andrew Salmon, 8-Jun-2011.) (Revised by Thierry Arnoux, 8-Mar-2017.)
Hypothesis
Ref Expression
ralcom4f.1
Assertion
Ref Expression
rexcom4f
Distinct variable group:   ,
Allowed substitution hints:   (,)   (,)

Proof of Theorem rexcom4f
StepHypRef Expression
1 ralcom4f.1 . . 3
2 nfcv 2592 . . 3
31, 2rexcomf 2950 . 2
4 rexv 3062 . . 3
54rexbii 2889 . 2
6 rexv 3062 . 2
73, 5, 63bitr3i 279 1
 Colors of variables: wff setvar class Syntax hints:   wb 188  wex 1663  wnfc 2579  wrex 2738  cvv 3045 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851  ax-10 1915  ax-11 1920  ax-12 1933  ax-13 2091  ax-ext 2431 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-tru 1447  df-ex 1664  df-nf 1668  df-sb 1798  df-clab 2438  df-cleq 2444  df-clel 2447  df-nfc 2581  df-ral 2742  df-rex 2743  df-v 3047 This theorem is referenced by: (None)
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