Theorem iinpw 4419

Description: The power class of an intersection in terms of indexed intersection. Exercise 24(a) of [Enderton] p. 33. (Contributed by NM, 29-Nov-2003.)

Assertion

Ref	Expression
iinpw

Distinct variable group:   ,

Proof of Theorem iinpw

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		ssint 4302	. . . 4
2		selpw 4019	. . . . 5
3	2	ralbii 2888	. . . 4
4	1, 3	bitr4i 252	. . 3
5		selpw 4019	. . 3
6		vex 3112	. . . 4
7		eliin 4336	. . . 4
8	6, 7	ax-mp 5	. . 3
9	4, 5, 8	3bitr4i 277	. 2
10	9	eqriv 2453	1

Syntax hints:  <->wb 184  =wceq 1395  e.wcel 1818  A.wral 2807  cvv 3109  C_wss 3475  ~Pcpw 4012  |^|cint 4286  |^|_ciin 4331

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-pw 4014  df-int 4287  df-iin 4333