Theorem reu3 3289

Description: A way to express restricted uniqueness. (Contributed by NM, 24-Oct-2006.)

Assertion

Ref	Expression
reu3

Distinct variable groups:   ,,   ,

Proof of Theorem reu3

Step	Hyp	Ref	Expression
1		reurex 3074	. . 3
2		reu6 3288	. . . 4
3		bi1 186	. . . . . 6
4	3	ralimi 2850	. . . . 5
5	4	reximi 2925	. . . 4
6	2, 5	sylbi 195	. . 3
7	1, 6	jca 532	. 2
8		rexex 2914	. . . 4
9	8	anim2i 569	. . 3
10		eu3v 2312	. . . 4
11		df-reu 2814	. . . 4
12		df-rex 2813	. . . . 5
13		df-ral 2812	. . . . . . 7
14		impexp 446	. . . . . . . 8
15	14	albii 1640	. . . . . . 7
16	13, 15	bitr4i 252	. . . . . 6
17	16	exbii 1667	. . . . 5
18	12, 17	anbi12i 697	. . . 4
19	10, 11, 18	3bitr4i 277	. . 3
20	9, 19	sylibr 212	. 2
21	7, 20	impbii 188	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  E.wex 1612  e.wcel 1818  E!weu 2282  A.wral 2807  E.wrex 2808  E!wreu 2809

This theorem is referenced by:  reu7  3294  2reu4a  32194

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-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-cleq 2449  df-clel 2452  df-ral 2812  df-rex 2813  df-reu 2814  df-rmo 2815