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Theorem iinpw 3888
 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
StepHypRef Expression
1 ssint 3776 . . . 4
2 vex 2730 . . . . . 6
32elpw 3536 . . . . 5
43ralbii 2531 . . . 4
51, 4bitr4i 245 . . 3
62elpw 3536 . . 3
7 eliin 3808 . . . 4
82, 7ax-mp 10 . . 3
95, 6, 83bitr4i 270 . 2
109eqriv 2250 1
 Colors of variables: wff set class Syntax hints:   wb 178   wceq 1619   wcel 1621  wral 2509  cvv 2727   wss 3078  cpw 3530  cint 3760  ciin 3804 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-ral 2513  df-v 2729  df-in 3085  df-ss 3089  df-pw 3532  df-int 3761  df-iin 3806
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