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Theorem iinpw 3939
 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 3823 . . . 4
2 vex 2715 . . . . . 6
32elpw 3549 . . . . 5
43ralbii 2463 . . . 4
51, 4bitr4i 186 . . 3
62elpw 3549 . . 3
7 eliin 3854 . . . 4
82, 7ax-mp 5 . . 3
95, 6, 83bitr4i 211 . 2
109eqriv 2154 1
 Colors of variables: wff set class Syntax hints:   wb 104   wceq 1335   wcel 2128  wral 2435  cvv 2712   wss 3102  cpw 3543  cint 3807  ciin 3850 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139 This theorem depends on definitions:  df-bi 116  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-ral 2440  df-v 2714  df-in 3108  df-ss 3115  df-pw 3545  df-int 3808  df-iin 3852 This theorem is referenced by: (None)
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