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Theorem pwin 4789
 Description: The power class of the intersection of two classes is the intersection of their power classes. Exercise 4.12(j) of [Mendelson] p. 235. (Contributed by NM, 23-Nov-2003.)
Assertion
Ref Expression
pwin

Proof of Theorem pwin
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 ssin 3719 . . . 4
2 selpw 4019 . . . . 5
3 selpw 4019 . . . . 5
42, 3anbi12i 697 . . . 4
5 selpw 4019 . . . 4
61, 4, 53bitr4i 277 . . 3
76ineqri 3691 . 2
87eqcomi 2470 1
 Colors of variables: wff setvar class Syntax hints:  /\wa 369  =wceq 1395  e.wcel 1818  i^icin 3474  C_wss 3475  ~Pcpw 4012 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-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-v 3111  df-in 3482  df-ss 3489  df-pw 4014
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