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Theorem iinpw 4027
 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.
StepHypRef Expression
1 ssint 3915 . . . 4
2 vex 2825 . . . . . 6
32elpw 3665 . . . . 5
43ralbii 2601 . . . 4
51, 4bitr4i 243 . . 3
62elpw 3665 . . 3
7 eliin 3947 . . . 4
82, 7ax-mp 8 . . 3
95, 6, 83bitr4i 268 . 2
109eqriv 2313 1
 Colors of variables: wff set class Syntax hints:   wb 176   wceq 1633   wcel 1701  wral 2577  cvv 2822   wss 3186  cpw 3659  cint 3899  ciin 3943 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1537  ax-5 1548  ax-17 1607  ax-9 1645  ax-8 1666  ax-6 1720  ax-7 1725  ax-11 1732  ax-12 1897  ax-ext 2297 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1533  df-nf 1536  df-sb 1640  df-clab 2303  df-cleq 2309  df-clel 2312  df-nfc 2441  df-ral 2582  df-v 2824  df-in 3193  df-ss 3200  df-pw 3661  df-int 3900  df-iin 3945
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