Theorem reusv5OLD 4662

Description: Two ways to express single-valuedness of a class expression (). (Contributed by NM, 16-Dec-2012.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
reusv5OLD

Distinct variable groups:   ,   ,,   ,

Proof of Theorem reusv5OLD

Step	Hyp	Ref	Expression
1		equid 1791	. . . . 5
2	1	biantru 505	. . . 4
3	2	exbii 1667	. . 3
4		n0 3794	. . 3
5		df-rex 2813	. . 3
6	3, 4, 5	3bitr4i 277	. 2
7		reusv1 4652	. . 3
8	1	a1bi 337	. . . . 5
9	8	ralbii 2888	. . . 4
10	9	reubii 3044	. . 3
11	9	rexbii 2959	. . 3
12	7, 10, 11	3bitr4g 288	. 2
13	6, 12	sylbi 195	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  E.wex 1612  e.wcel 1818  =/=wne 2652  A.wral 2807  E.wrex 2808  E!wreu 2809  c0 3784

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-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-reu 2814  df-rmo 2815  df-v 3111  df-dif 3478  df-nul 3785