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Theorem unissi 4119
Description: Subclass relationship for subclass union. Inference form of uniss 4117. (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
StepHypRef Expression
1 unissi.1 . 2  |-  A  C_  B
2 uniss 4117 . 2  |-  ( A 
C_  B  ->  U. A  C_ 
U. B )
31, 2ax-mp 5 1  |-  U. A  C_ 
U. B
Colors of variables: wff setvar class
Syntax hints:    C_ wss 3333   U.cuni 4096
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1591  ax-4 1602  ax-5 1670  ax-6 1708  ax-7 1728  ax-10 1775  ax-11 1780  ax-12 1792  ax-13 1943  ax-ext 2423
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1372  df-ex 1587  df-nf 1590  df-sb 1701  df-clab 2430  df-cleq 2436  df-clel 2439  df-nfc 2573  df-v 2979  df-in 3340  df-ss 3347  df-uni 4097
This theorem is referenced by:  unidif  4130  unixpss  4960  riotassuniOLD  6094  unifpw  7619  fiuni  7683  rankuni  8075  fin23lem29  8515  fin23lem30  8516  fin1a2lem12  8585  prdsds  14407  psss  15389  tgval2  18566  eltg4i  18570  unitg  18577  ntrss2  18666  isopn3  18675  mretopd  18701  ordtbas  18801  cmpcov2  18998  tgcmp  19009  alexsublem  19621  alexsubALTlem3  19626  alexsubALTlem4  19627  cldsubg  19686  bndth  20535  uniioombllem4  21071  uniioombllem5  21072  cvmscld  27167  mblfinlem3  28435  mblfinlem4  28436  ismblfin  28437  mbfresfi  28443  fnessref  28570  comppfsc  28584  cover2  28612
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