Theorem unissi 3858

Description: Subclass relationship for subclass union. Inference form of uniss 3856. (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 3856	. 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 3153   U.cuni 3835

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 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2175

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-nfc 2325  df-v 2762  df-in 3159  df-ss 3166  df-uni 3836

This theorem is referenced by:  unidif  3867  unixpss  4772  tfrcllemssrecs  6405  tgvalex  12874  tgval2  14219  eltg4i  14223  ntrss2  14289  isopn3  14293