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Theorem pwin 4442
 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 3520 . . . 4
2 vex 2916 . . . . . 6
32elpw 3762 . . . . 5
42elpw 3762 . . . . 5
53, 4anbi12i 679 . . . 4
62elpw 3762 . . . 4
71, 5, 63bitr4i 269 . . 3
87ineqri 3491 . 2
98eqcomi 2405 1
 Colors of variables: wff set class Syntax hints:   wa 359   wceq 1649   wcel 1721   cin 3276   wss 3277  cpw 3756 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2382 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2526  df-v 2915  df-in 3284  df-ss 3291  df-pw 3758
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