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Theorem pwin 4487
 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 3563 . . . 4
2 vex 2959 . . . . . 6
32elpw 3805 . . . . 5
42elpw 3805 . . . . 5
53, 4anbi12i 679 . . . 4
62elpw 3805 . . . 4
71, 5, 63bitr4i 269 . . 3
87ineqri 3534 . 2
98eqcomi 2440 1
 Colors of variables: wff set class Syntax hints:   wa 359   wceq 1652   wcel 1725   cin 3319   wss 3320  cpw 3799 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-v 2958  df-in 3327  df-ss 3334  df-pw 3801
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