Theorem intmin4 4316

Description: Elimination of a conjunct in a class intersection. (Contributed by NM, 31-Jul-2006.)

Assertion

Ref	Expression
intmin4

Distinct variable group:   ,

Proof of Theorem intmin4

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		ssintab 4303	. . . 4
2		simpr 461	. . . . . . . 8
3		ancr 549	. . . . . . . 8
4	2, 3	impbid2 204	. . . . . . 7
5	4	imbi1d 317	. . . . . 6
6	5	alimi 1633	. . . . 5
7		albi 1639	. . . . 5
8	6, 7	syl 16	. . . 4
9	1, 8	sylbi 195	. . 3
10		vex 3112	. . . 4
11	10	elintab 4297	. . 3
12	10	elintab 4297	. . 3
13	9, 11, 12	3bitr4g 288	. 2
14	13	eqrdv 2454	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  =wceq 1395  e.wcel 1818  {cab 2442  C_wss 3475  |^|cint 4286

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-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-v 3111  df-in 3482  df-ss 3489  df-int 4287