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Theorem sspwimpALT2 29040
 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 2959 . . . 4
2 elpwi 3807 . . . . 5
3 id 20 . . . . 5
42, 3sylan9ssr 3362 . . . 4
5 elpwg 3806 . . . . 5
65biimpar 472 . . . 4
71, 4, 6sylancr 645 . . 3
87ex 424 . 2
98ssrdv 3354 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   wcel 1725  cvv 2956   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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