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Theorem unissd 3728
Description: Subclass relationship for subclass union. Deduction form of uniss 3725. (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 3725 . 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 3039   U.cuni 3704
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097
This theorem depends on definitions:  df-bi 116  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-v 2660  df-in 3045  df-ss 3052  df-uni 3705
This theorem is referenced by:  iotanul  5071  tfrlemibfn  6191  tfrlemiubacc  6193  tfr1onlemssrecs  6202  tfr1onlembfn  6207  tfr1onlemubacc  6209  tfrcllemssrecs  6215  tfrcllembfn  6220  tfrcllemubacc  6222  fiuni  6832  eltg3i  12131  unitg  12137  tgss  12138  ntrss  12194
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