Theorem unss2 3674

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

Step	Hyp	Ref	Expression
1		unss1 3672	. 2
2		uncom 3647	. 2
3		uncom 3647	. 2
4	1, 2, 3	3sstr4g 3544	1

Syntax hints:  ->wi 4  u.cun 3473  C_wss 3475

This theorem is referenced by:  unss12  3675  ord3ex  4642  xpider  7401  fin1a2lem13  8813  canthp1lem2  9052  uniioombllem3  21994  volcn  22015  dvres2lem  22314  bnj1413  34091  bnj1408  34092

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111  df-un 3480  df-in 3482  df-ss 3489