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Theorem pwunss 4314
 Description: The power class of the union of two classes includes the union of their power classes. Exercise 4.12(k) of [Mendelson] p. 235. (Contributed by NM, 23-Nov-2003.)
Assertion
Ref Expression
pwunss

Proof of Theorem pwunss
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 ssun 3367 . . 3
2 elun 3329 . . . 4
3 vex 2804 . . . . . 6
43elpw 3644 . . . . 5
53elpw 3644 . . . . 5
64, 5orbi12i 507 . . . 4
72, 6bitri 240 . . 3
83elpw 3644 . . 3
91, 7, 83imtr4i 257 . 2
109ssriv 3197 1
 Colors of variables: wff set class Syntax hints:   wo 357   wcel 1696   cun 3163   wss 3165  cpw 3638 This theorem is referenced by:  pwundif  4316  pwun  4318  pwundif2  23202 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-un 3170  df-in 3172  df-ss 3179  df-pw 3640
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