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Theorem pwundif 4482
 Description: Break up the power class of a union into a union of smaller classes. (Contributed by NM, 25-Mar-2007.) (Proof shortened by Thierry Arnoux, 20-Dec-2016.)
Assertion
Ref Expression
pwundif

Proof of Theorem pwundif
StepHypRef Expression
1 undif1 3695 . 2
2 pwunss 4480 . . . . 5
3 unss 3513 . . . . 5
42, 3mpbir 201 . . . 4
54simpli 445 . . 3
6 ssequn2 3512 . . 3
75, 6mpbi 200 . 2
81, 7eqtr2i 2456 1
 Colors of variables: wff set class Syntax hints:   wa 359   wceq 1652   cdif 3309   cun 3310   wss 3312  cpw 3791 This theorem is referenced by:  pwfilem  7393 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 2416 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 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-pw 3793
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