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Theorem unissd 3851
Description: Subclass relationship for subclass union. Deduction form of uniss 3848. (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 3848 . 2  |-  ( A 
C_  B  ->  U. A  C_ 
U. B )
31, 2syl 15 1  |-  ( ph  ->  U. A  C_  U. B
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    C_ wss 3152   U.cuni 3827
This theorem is referenced by:  incexc  12296  incexc2  12297  acsmapd  14281  acsmap2d  14282
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-v 2790  df-in 3159  df-ss 3166  df-uni 3828
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