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Theorem sspwimp 27384
 Description: If a class is a subclass of another class, then its power class is a subclass of that other class's power class. Left-to-right implication of Exercise 18 of [TakeutiZaring] p. 18. sspwimp 27384, using conventional notation, was translated from virtual deduction form, sspwimpVD 27385, using a translation program. (Contributed by Alan Sare, 23-Apr-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
sspwimp

Proof of Theorem sspwimp
StepHypRef Expression
1 vex 2730 . . . . . . 7
21a1i 12 . . . . . 6
3 id 21 . . . . . . 7
4 id 21 . . . . . . . 8
5 elpwi 3538 . . . . . . . 8
64, 5syl 17 . . . . . . 7
7 sstr 3108 . . . . . . . 8
87ancoms 441 . . . . . . 7
93, 6, 8syl2an 465 . . . . . 6
102, 9elpwgded 27023 . . . . . 6
112, 9, 10uun0.1 27243 . . . . 5
1211ex 425 . . . 4
1312alrimiv 2012 . . 3
14 dfss2 3092 . . . 4
1514biimpri 199 . . 3
1613, 15syl 17 . 2
1716iin1 27033 1
 Colors of variables: wff set class Syntax hints:   wi 6   wa 360   wtru 1312  wal 1532   wcel 1621  cvv 2727   wss 3078  cpw 3530 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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