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Theorem unissi 4002
Description: Subclass relationship for subclass union. Inference form of uniss 4000. (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 4000 . 2  |-  ( A 
C_  B  ->  U. A  C_ 
U. B )
31, 2ax-mp 8 1  |-  U. A  C_ 
U. B
Colors of variables: wff set class
Syntax hints:    C_ wss 3284   U.cuni 3979
This theorem is referenced by:  unidif  4011  unixpss  4951  riotassuni  6551  unifpw  7371  fiuni  7395  rankuni  7749  fin23lem29  8181  fin23lem30  8182  fin1a2lem12  8251  prdsds  13645  psss  14605  tgval2  16980  eltg4i  16984  unitg  16991  ntrss2  17080  isopn3  17089  mretopd  17115  ordtbas  17214  cmpcov2  17411  tgcmp  17422  alexsublem  18032  alexsubALTlem3  18037  alexsubALTlem4  18038  cldsubg  18097  bndth  18940  uniioombllem4  19435  uniioombllem5  19436  cvmscld  24917  mblfinlem2  26148  mblfinlem3  26149  ismblfin  26150  mbfresfi  26156  fnessref  26267  comppfsc  26281  cover2  26309
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2389
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2395  df-cleq 2401  df-clel 2404  df-nfc 2533  df-v 2922  df-in 3291  df-ss 3298  df-uni 3980
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