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Theorem unissd 3833
Description: Subclass relationship for subclass union. Deduction form of uniss 3830. (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 3830 . 2  |-  ( A 
C_  B  ->  U. A  C_ 
U. B )
31, 2syl 14 1  |-  ( ph  ->  U. A  C_  U. B
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    C_ wss 3129   U.cuni 3809
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-v 2739  df-in 3135  df-ss 3142  df-uni 3810
This theorem is referenced by:  iotanul  5192  tfrlemibfn  6326  tfrlemiubacc  6328  tfr1onlemssrecs  6337  tfr1onlembfn  6342  tfr1onlemubacc  6344  tfrcllemssrecs  6350  tfrcllembfn  6355  tfrcllemubacc  6357  fiuni  6974  eltg3i  13427  unitg  13433  tgss  13434  ntrss  13490
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