Theorem unissi 3911

Description: Subclass relationship for subclass union. Inference form of uniss 3909. (Contributed by David Moews, 1-May-2017.)

Hypothesis

Ref	Expression
unissi.1	|- A C_ B

Assertion

Ref	Expression
unissi	|- U. A C_ U. B

Proof of Theorem unissi

Step	Hyp	Ref	Expression
1		unissi.1	. 2 |- A C_ B
2		uniss 3909	. 2 |- ( A C_ B -> U. A C_ U. B )
3	1, 2	ax-mp 5	1 |- U. A C_ U. B

Syntax hints:   C_ wss 3197   U.cuni 3888

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 714  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-10 1551  ax-11 1552  ax-i12 1553  ax-bndl 1555  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211

This theorem depends on definitions:  df-bi 117  df-tru 1398  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-nfc 2361  df-v 2801  df-in 3203  df-ss 3210  df-uni 3889

This theorem is referenced by:  unidif  3920  unixpss  4832  tfrcllemssrecs  6498  tgvalex  13296  tgval2  14725  eltg4i  14729  ntrss2  14795  isopn3  14799