Theorem unissd 3755

Description: Subclass relationship for subclass union. Deduction form of uniss 3752. (Contributed by David Moews, 1-May-2017.)

Hypothesis

Ref	Expression
unissd.1	|- ( ph -> A C_ B )

Assertion

Ref	Expression
unissd	|- ( ph -> U. A C_ U. B )

Proof of Theorem unissd

Step	Hyp	Ref	Expression
1		unissd.1	. 2 |- ( ph -> A C_ B )
2		uniss 3752	. 2 |- ( A C_ B -> U. A C_ U. B )
3	1, 2	syl 14	1 |- ( ph -> U. A C_ U. B )

Syntax hints:   -> wi 4   C_ wss 3066   U.cuni 3731

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119

This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-v 2683  df-in 3072  df-ss 3079  df-uni 3732

This theorem is referenced by:  iotanul  5098  tfrlemibfn  6218  tfrlemiubacc  6220  tfr1onlemssrecs  6229  tfr1onlembfn  6234  tfr1onlemubacc  6236  tfrcllemssrecs  6242  tfrcllembfn  6247  tfrcllemubacc  6249  fiuni  6859  eltg3i  12214  unitg  12220  tgss  12221  ntrss  12277