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Theorem pwundifOLD 4317
 Description: Break up the power class of a union into a union of smaller classes. Obsolete as of 20-Dec-2016. (Contributed by NM, 25-Mar-2007.) (New usage is discouraged.)
Assertion
Ref Expression
pwundifOLD

Proof of Theorem pwundifOLD
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 vex 2804 . . . 4
21elpw 3644 . . 3
3 pm2.1 406 . . . . 5
4 ordir 835 . . . . 5
53, 4mpbiran2 885 . . . 4
6 elun 3329 . . . . 5
7 eldif 3175 . . . . . . 7
81elpw 3644 . . . . . . . . 9
98notbii 287 . . . . . . . 8
102, 9anbi12i 678 . . . . . . 7
117, 10bitri 240 . . . . . 6
1211, 8orbi12i 507 . . . . 5
136, 12bitr2i 241 . . . 4
14 id 19 . . . . . 6
15 ssun3 3353 . . . . . 6
1614, 15jaoi 368 . . . . 5
17 orc 374 . . . . 5
1816, 17impbii 180 . . . 4
195, 13, 183bitr3ri 267 . . 3
202, 19bitri 240 . 2
2120eqriv 2293 1
 Colors of variables: wff set class Syntax hints:   wn 3   wo 357   wa 358   wceq 1632   wcel 1696   cdif 3162   cun 3163   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-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-pw 3640
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