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

Step	Hyp	Ref	Expression
1		pm2.04 82	. . 3
2	1	ralimi2 2847	. 2
3		pm2.04 82	. . 3
4	3	ralimi2 2847	. 2
5	2, 4	impbii 188	1

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