Theorem ralcomf 3016

Description: Commutation of restricted universal quantifiers. (Contributed by Mario Carneiro, 14-Oct-2016.)

Hypotheses

Ref	Expression
ralcomf.1
ralcomf.2

Assertion

Ref	Expression
ralcomf

Distinct variable group:   ,

Proof of Theorem ralcomf

Step	Hyp	Ref	Expression
1		ancomst 452	. . . 4
2	1	2albii 1641	. . 3
3		alcom 1845	. . 3
4	2, 3	bitri 249	. 2
5		ralcomf.1	. . 3
6	5	r2alf 2833	. 2
7		ralcomf.2	. . 3
8	7	r2alf 2833	. 2
9	4, 6, 8	3bitr4i 277	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  e.wcel 1818  F/_wnfc 2605  A.wral 2807

This theorem is referenced by:  ralcom  3018  ssiinf  4379  ralcom4f  27375

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-ex 1613  df-nf 1617  df-sb 1740  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812