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Theorem sspwimpALT2 27395
 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. Proof derived by completeusersproof.c from User's Proof in VirtualDeductionProofs.txt. The User's Proof in html format is displayed in http://www.virtualdeduction.com/sspwimpaltvd.html. (Contributed by Alan Sare, 11-Sep-2016.)
Assertion
Ref Expression
sspwimpALT2

Proof of Theorem sspwimpALT2
StepHypRef Expression
1 vex 2730 . . . . . 6
2 id 21 . . . . . . 7
3 id 21 . . . . . . . 8
4 elpwi 3538 . . . . . . . 8
53, 4syl 17 . . . . . . 7
6 sstr2 3107 . . . . . . . 8
76impcom 421 . . . . . . 7
82, 5, 7syl2an 465 . . . . . 6
9 elpwg 3537 . . . . . . 7
109biimpar 473 . . . . . 6
111, 8, 10sylancr 647 . . . . 5
1211ex 425 . . . 4
1312alrimiv 2012 . . 3
14 dfss2 3092 . . . 4
1514biimpri 199 . . 3
1613, 15syl 17 . 2
1716idi 2 1
 Colors of variables: wff set class Syntax hints:   wi 6   wa 360  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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