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Theorem pwin 4190
 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
StepHypRef Expression
1 ssin 3298 . . . 4
2 vex 2730 . . . . . 6
32elpw 3536 . . . . 5
42elpw 3536 . . . . 5
53, 4anbi12i 681 . . . 4
62elpw 3536 . . . 4
71, 5, 63bitr4i 270 . . 3
87ineqri 3270 . 2
98eqcomi 2257 1
 Colors of variables: wff set class Syntax hints:   wa 360   wceq 1619   wcel 1621   cin 3077   wss 3078  cpw 3530 This theorem is referenced by:  selsubf  25156  selsubf3  25157 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-v 2729  df-in 3085  df-ss 3089  df-pw 3532
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