Theorem reuun2 3780

Description: Transfer uniqueness to a smaller or larger class. (Contributed by NM, 21-Oct-2005.)

Assertion

Ref	Expression
reuun2

Distinct variable groups:   ,   ,

Proof of Theorem reuun2

Step	Hyp	Ref	Expression
1		df-rex 2813	. . 3
2		euor2 2333	. . 3
3	1, 2	sylnbi 306	. 2
4		df-reu 2814	. . 3
5		elun 3644	. . . . . 6
6	5	anbi1i 695	. . . . 5
7		andir 868	. . . . . 6
8		orcom 387	. . . . . 6
9	7, 8	bitri 249	. . . . 5
10	6, 9	bitri 249	. . . 4
11	10	eubii 2306	. . 3
12	4, 11	bitri 249	. 2
13		df-reu 2814	. 2
14	3, 12, 13	3bitr4g 288	1

Syntax hints:  -.wn 3  ->wi 4  <->wb 184  \/wo 368  /\wa 369  E.wex 1612  e.wcel 1818  E!weu 2282  E.wrex 2808  E!wreu 2809  u.cun 3473

This theorem is referenced by:  hdmap14lem4a  37601

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-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rex 2813  df-reu 2814  df-v 3111  df-un 3480