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Theorem ralcom3 3023
Description: A commutation law for restricted universal quantifiers that swaps the domains of the restriction. (Contributed by NM, 22-Feb-2004.)
Assertion
Ref Expression
ralcom3

Proof of Theorem ralcom3
StepHypRef Expression
1 pm2.04 82 . . 3
21ralimi2 2847 . 2
3 pm2.04 82 . . 3
43ralimi2 2847 . 2
52, 4impbii 188 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  e.wcel 1818  A.wral 2807
This theorem is referenced by:  tgss2  19489  ist1-3  19850  isreg2  19878
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631
This theorem depends on definitions:  df-bi 185  df-ral 2812
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