Theorem unssi 3678

Description: An inference showing the union of two subclasses is a subclass. (Contributed by Raph Levien, 10-Dec-2002.)

Hypotheses

Ref	Expression
unssi.1
unssi.2

Assertion

Ref	Expression
unssi

Proof of Theorem unssi

Step	Hyp	Ref	Expression
1		unssi.1	. . 3
2		unssi.2	. . 3
3	1, 2	pm3.2i 455	. 2
4		unss 3677	. 2
5	3, 4	mpbi 208	1

Syntax hints:  /\wa 369  u.cun 3473  C_wss 3475

This theorem is referenced by:  dmrnssfld  5266  tc2  8194  pwxpndom2  9064  ltrelxr  9669  nn0ssre  10824  nn0ssz  10910  dfle2  11382  difreicc  11681  hashxrcl  12429  ramxrcl  14535  strlemor1  14724  strleun  14727  cssincl  18719  leordtval2  19713  lecldbas  19720  comppfsc  20033  aalioulem2  22729  taylfval  22754  axlowdimlem10  24254  konigsberg  24987  shunssji  26287  shsval3i  26306  shjshsi  26410  spanuni  26462  sshhococi  26464  esumcst  28071  hashf2  28090  sxbrsigalem3  28243  signswch  28518  mblfinlem3  30053  mblfinlem4  30054  cncfiooicclem1  31696  fourierdlem62  31951  bj-unrab  34494  bj-tagss  34538  hdmapevec  37565

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