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Theorem unss2 3657
 Description: Subclass law for union of classes. Exercise 7 of [TakeutiZaring] p. 18. (Contributed by NM, 14-Oct-1999.)
Assertion
Ref Expression
unss2

Proof of Theorem unss2
StepHypRef Expression
1 unss1 3655 . 2
2 uncom 3630 . 2
3 uncom 3630 . 2
41, 2, 33sstr4g 3527 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   cun 3456   wss 3458 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1603  ax-4 1616  ax-5 1689  ax-6 1732  ax-7 1774  ax-10 1821  ax-11 1826  ax-12 1838  ax-13 1983  ax-ext 2419 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1384  df-ex 1598  df-nf 1602  df-sb 1725  df-clab 2427  df-cleq 2433  df-clel 2436  df-nfc 2591  df-v 3095  df-un 3463  df-in 3465  df-ss 3472 This theorem is referenced by:  unss12  3658  ord3ex  4623  xpider  7380  fin1a2lem13  8790  canthp1lem2  9029  uniioombllem3  21860  volcn  21881  dvres2lem  22180  bnj1413  33798  bnj1408  33799
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