Theorem unissi 3603

Description: Subclass relationship for subclass union. Inference form of uniss 3601. (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 3601	. 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 2917   U.cuni 3580

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022

This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-in 2924  df-ss 2931  df-uni 3581

This theorem is referenced by:  unidif  3612  unixpss  4451