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Theorem ralcom4f 28096
 Description: Commutation of restricted and unrestricted universal quantifiers. (Contributed by NM, 26-Mar-2004.) (Proof shortened by Andrew Salmon, 8-Jun-2011.) (Revised by Thierry Arnoux, 8-Mar-2017.)
Hypothesis
Ref Expression
ralcom4f.1
Assertion
Ref Expression
ralcom4f
Distinct variable group:   ,
Allowed substitution hints:   (,)   (,)

Proof of Theorem ralcom4f
StepHypRef Expression
1 ralcom4f.1 . . 3
2 nfcv 2584 . . 3
31, 2ralcomf 2987 . 2
4 ralv 3095 . . 3
54ralbii 2856 . 2
6 ralv 3095 . 2
73, 5, 63bitr3i 278 1
 Colors of variables: wff setvar class Syntax hints:   wb 187  wal 1435  wnfc 2570  wral 2775  cvv 3081 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1839  ax-10 1887  ax-11 1892  ax-12 1905  ax-13 2053  ax-ext 2400 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1787  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2572  df-ral 2780  df-v 3083 This theorem is referenced by: (None)
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