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Theorem sspwimpALT2 29021
 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
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 vex 2804 . . . . . 6
2 id 19 . . . . . . 7
3 id 19 . . . . . . . 8
4 elpwi 3646 . . . . . . . 8
53, 4syl 15 . . . . . . 7
6 sstr2 3199 . . . . . . . 8
76impcom 419 . . . . . . 7
82, 5, 7syl2an 463 . . . . . 6
9 elpwg 3645 . . . . . . 7
109biimpar 471 . . . . . 6
111, 8, 10sylancr 644 . . . . 5
1211ex 423 . . . 4
1312alrimiv 1621 . . 3
14 dfss2 3182 . . . 4
1514biimpri 197 . . 3
1613, 15syl 15 . 2
1716idi 2 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 358  wal 1530   wcel 1696  cvv 2801   wss 3165  cpw 3638 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-v 2803  df-in 3172  df-ss 3179  df-pw 3640
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