MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  unissd Unicode version

Theorem unissd 3867
Description: Subclass relationship for subclass union. Deduction form of uniss 3864. (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 3864 . 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 3165   U.cuni 3843
This theorem is referenced by:  incexc  12312  incexc2  12313  acsmapd  14297  acsmap2d  14298
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-v 2803  df-in 3172  df-ss 3179  df-uni 3844
  Copyright terms: Public domain W3C validator