Theorem r3al 2837

Description: Triple restricted universal quantification. (Contributed by NM, 19-Nov-1995.) (Proof shortened by Wolf Lammen, 30-Dec-2019.)

Assertion

Ref	Expression
r3al

Distinct variable groups:   ,,   ,,   ,

Proof of Theorem r3al

Step	Hyp	Ref	Expression
1		r2al 2835	. 2
2		19.21v 1729	. . . 4
3		df-3an 975	. . . . . . 7
4	3	imbi1i 325	. . . . . 6
5		impexp 446	. . . . . 6
6	4, 5	bitri 249	. . . . 5
7	6	albii 1640	. . . 4
8		df-ral 2812	. . . . 5
9	8	imbi2i 312	. . . 4
10	2, 7, 9	3bitr4ri 278	. . 3
11	10	2albii 1641	. 2
12	1, 11	bitri 249	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  /\w3a 973  A.wal 1393  e.wcel 1818  A.wral 2807

This theorem is referenced by:  pocl  4812  dfwe2  6617  isass  25318

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

This theorem depends on definitions:  df-bi 185  df-an 371  df-3an 975  df-ex 1613  df-ral 2812