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Theorem unissd 4269
Description: Subclass relationship for subclass union. Deduction form of uniss 4266. (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 4266 . 2  |-  ( A 
C_  B  ->  U. A  C_ 
U. B )
31, 2syl 16 1  |-  ( ph  ->  U. A  C_  U. B
)
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    C_ wss 3476   U.cuni 4245
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-v 3115  df-in 3483  df-ss 3490  df-uni 4246
This theorem is referenced by:  dffv2  5940  onfununi  7012  fiuni  7888  dfac2a  8510  incexc  13612  incexc2  13613  isacs1i  14912  isacs3lem  15653  acsmapd  15665  acsmap2d  15666  dprd2da  16893  eltg3i  19257  unitg  19263  tgss  19264  tgcmp  19695  cmpfi  19702  alexsubALTlem4  20313  ptcmplem3  20317  ustbas2  20491  uniioombllem3  21757  shsupunss  25968  dya2iocucvr  27923  cvmscld  28386  nofulllem3  29069  onsucsuccmpi  29513  fnemeet1  29815  fnejoin1  29817  heibor1  29937  heiborlem10  29947  hbt  30711
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