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Theorem pwundifss 4165
 Description: Break up the power class of a union into a union of smaller classes. (Contributed by Jim Kingdon, 30-Sep-2018.)
Assertion
Ref Expression
pwundifss

Proof of Theorem pwundifss
StepHypRef Expression
1 undif1ss 3401 . 2
2 pwunss 4163 . . . . 5
3 unss 3214 . . . . 5
42, 3mpbir 145 . . . 4
54simpli 110 . . 3
6 ssequn2 3213 . . 3
75, 6mpbi 144 . 2
81, 7sseqtri 3095 1
 Colors of variables: wff set class Syntax hints:   wa 103   wceq 1312   cdif 3032   cun 3033   wss 3035  cpw 3474 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 586  ax-in2 587  ax-io 681  ax-5 1404  ax-7 1405  ax-gen 1406  ax-ie1 1450  ax-ie2 1451  ax-8 1463  ax-10 1464  ax-11 1465  ax-i12 1466  ax-bndl 1467  ax-4 1468  ax-17 1487  ax-i9 1491  ax-ial 1495  ax-i5r 1496  ax-ext 2095 This theorem depends on definitions:  df-bi 116  df-tru 1315  df-nf 1418  df-sb 1717  df-clab 2100  df-cleq 2106  df-clel 2109  df-nfc 2242  df-v 2657  df-dif 3037  df-un 3039  df-in 3041  df-ss 3048  df-pw 3476 This theorem is referenced by: (None)
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