Theorem 2ralor 3027

Description: Distribute restricted universal quantification over "or". (Contributed by Jeff Madsen, 19-Jun-2010.)

Assertion

Ref	Expression
2ralor

Distinct variable groups:   ,   ,   ,   ,   ,

Proof of Theorem 2ralor

Step	Hyp	Ref	Expression
1		rexnal 2905	. . . 4
2		rexnal 2905	. . . 4
3	1, 2	anbi12i 697	. . 3
4		ioran 490	. . . . . . 7
5	4	rexbii 2959	. . . . . 6
6		rexnal 2905	. . . . . 6
7	5, 6	bitr3i 251	. . . . 5
8	7	rexbii 2959	. . . 4
9		reeanv 3025	. . . 4
10		rexnal 2905	. . . 4
11	8, 9, 10	3bitr3ri 276	. . 3
12		ioran 490	. . 3
13	3, 11, 12	3bitr4i 277	. 2
14	13	con4bii 297	1

Syntax hints:  -.wn 3  <->wb 184  \/wo 368  /\wa 369  A.wral 2807  E.wrex 2808

This theorem is referenced by:  ispridl2  30435

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-or 370  df-an 371  df-ex 1613  df-nf 1617  df-ral 2812  df-rex 2813