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Theorem iinpw 4391
 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 4271 . . . 4
2 selpw 3988 . . . . 5
32ralbii 2853 . . . 4
41, 3bitr4i 255 . . 3
5 selpw 3988 . . 3
6 vex 3083 . . . 4
7 eliin 4305 . . . 4
86, 7ax-mp 5 . . 3
94, 5, 83bitr4i 280 . 2
109eqriv 2418 1
 Colors of variables: wff setvar class Syntax hints:   wb 187   wceq 1437   wcel 1872  wral 2771  cvv 3080   wss 3436  cpw 3981  cint 4255  ciin 4300 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2057  ax-ext 2401 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2568  df-ral 2776  df-v 3082  df-in 3443  df-ss 3450  df-pw 3983  df-int 4256  df-iin 4302 This theorem is referenced by: (None)
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