Theorem 3reeanv 3026

Description: Rearrange three restricted existential quantifiers. (Contributed by Jeff Madsen, 11-Jun-2010.)

Assertion

Ref	Expression
3reeanv

Distinct variable groups:   ,,   ,,   ,,   ,   ,,   ,,

Proof of Theorem 3reeanv

Step	Hyp	Ref	Expression
1		r19.41v 3009	. . 3
2		reeanv 3025	. . . 4
3	2	anbi1i 695	. . 3
4	1, 3	bitri 249	. 2
5		df-3an 975	. . . . 5
6	5	2rexbii 2960	. . . 4
7		reeanv 3025	. . . 4
8	6, 7	bitri 249	. . 3
9	8	rexbii 2959	. 2
10		df-3an 975	. 2
11	4, 9, 10	3bitr4i 277	1

Syntax hints:  <->wb 184  /\wa 369  /\w3a 973  E.wrex 2808

This theorem is referenced by:  imasmnd2  15957  imasgrp2  16185  imasring  17268  axeuclid  24266  lshpkrlem6  34840

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

This theorem depends on definitions:  df-bi 185  df-an 371  df-3an 975  df-ex 1613  df-nf 1617  df-ral 2812  df-rex 2813