Theorem unissi 3624

Description: Subclass relationship for subclass union. Inference form of uniss 3622. (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 3622	. 2 |- ( A C_ B -> U. A C_ U. B )
3	1, 2	ax-mp 7	1 |- U. A C_ U. B

Syntax hints:   C_ wss 2973   U.cuni 3601

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 662  ax-5 1376  ax-7 1377  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-10 1436  ax-11 1437  ax-i12 1438  ax-bndl 1439  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-i5r 1468  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-tru 1287  df-nf 1390  df-sb 1686  df-clab 2068  df-cleq 2074  df-clel 2077  df-nfc 2208  df-v 2603  df-in 2979  df-ss 2986  df-uni 3602

This theorem is referenced by:  unidif  3633  unixpss  4469