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Theorem unissd 4181
Description: Subclass relationship for subclass union. Deduction form of uniss 4178. (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
StepHypRef Expression
1 unissd.1 . 2  |-  ( ph  ->  A  C_  B )
2 uniss 4178 . 2  |-  ( A 
C_  B  ->  U. A  C_ 
U. B )
31, 2syl 17 1  |-  ( ph  ->  U. A  C_  U. B
)
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    C_ wss 3374   U.cuni 4157
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2058  ax-ext 2403
This theorem depends on definitions:  df-bi 188  df-an 372  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2410  df-cleq 2416  df-clel 2419  df-nfc 2553  df-v 3019  df-in 3381  df-ss 3388  df-uni 4158
This theorem is referenced by:  dffv2  5893  onfununi  7010  fiuni  7890  dfac2a  8506  incexc  13833  incexc2  13834  isacs1i  15501  isacs3lem  16350  acsmapd  16362  acsmap2d  16363  dprdres  17599  dprd2da  17613  eltg3i  19913  unitg  19919  unitgOLD  19920  tgss  19921  tgcmp  20353  cmpfi  20360  alexsubALTlem4  21002  ptcmplem3  21006  ustbas2  21177  uniioombllem3  22480  shsupunss  26936  locfinref  28615  cmpcref  28624  dya2iocucvr  29053  omssubadd  29075  omssubaddOLD  29079  carsggect  29097  cvmscld  29943  nofulllem3  30537  fnemeet1  30966  fnejoin1  30968  onsucsuccmpi  31047  heibor1  32049  heiborlem10  32059  hbt  35902  caragenuni  38183  caragendifcl  38186
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