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Theorem pwun 4446
 Description: The power class of the union of two classes equals the union of their power classes, iff one class is a subclass of the other. Part of Exercise 7(b) of [Enderton] p. 28. (Contributed by NM, 23-Nov-2003.)
Assertion
Ref Expression
pwun

Proof of Theorem pwun
StepHypRef Expression
1 pwunss 4443 . . 3
21biantru 492 . 2
3 pwssun 4444 . 2
4 eqss 3320 . 2
52, 3, 43bitr4i 269 1
 Colors of variables: wff set class Syntax hints:   wb 177   wo 358   wa 359   wceq 1649   cun 3275   wss 3277  cpw 3756 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-14 1725  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2382  ax-sep 4285  ax-pr 4358 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2526  df-v 2915  df-un 3282  df-in 3284  df-ss 3291  df-pw 3758  df-sn 3777  df-pr 3778
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