Theorem unissi 3873

Description: Subclass relationship for subclass union. Inference form of uniss 3871. (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 3871	. 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 3166   U.cuni 3850

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 711  ax-5 1470  ax-7 1471  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-10 1528  ax-11 1529  ax-i12 1530  ax-bndl 1532  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-i5r 1558  ax-ext 2187

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-nf 1484  df-sb 1786  df-clab 2192  df-cleq 2198  df-clel 2201  df-nfc 2337  df-v 2774  df-in 3172  df-ss 3179  df-uni 3851

This theorem is referenced by:  unidif  3882  unixpss  4788  tfrcllemssrecs  6438  tgvalex  13095  tgval2  14523  eltg4i  14527  ntrss2  14593  isopn3  14597