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Theorem unissd 3651
Description: Subclass relationship for subclass union. Deduction form of uniss 3648. (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 3648 . 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 2984   U.cuni 3627
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-v 2614  df-in 2990  df-ss 2997  df-uni 3628
This theorem is referenced by:  iotanul  4948  tfrlemibfn  6024  tfrlemiubacc  6026  tfr1onlemssrecs  6035  tfr1onlembfn  6040  tfr1onlemubacc  6042  tfrcllemssrecs  6048  tfrcllembfn  6053  tfrcllemubacc  6055
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