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Theorem pwin 4045
 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 3195 . . . 4
2 vex 2605 . . . . . 6
32elpw 3396 . . . . 5
42elpw 3396 . . . . 5
53, 4anbi12i 448 . . . 4
62elpw 3396 . . . 4
71, 5, 63bitr4i 210 . . 3
87ineqri 3166 . 2
98eqcomi 2086 1
 Colors of variables: wff set class Syntax hints:   wa 102   wceq 1285   wcel 1434   cin 2973   wss 2974  cpw 3390 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-v 2604  df-in 2980  df-ss 2987  df-pw 3392 This theorem is referenced by: (None)
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