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Theorem unissi 3729
Description: Subclass relationship for subclass union. Inference form of uniss 3727. (Contributed by David Moews, 1-May-2017.)
Hypothesis
Ref Expression
unissi.1  |-  A  C_  B
Assertion
Ref Expression
unissi  |-  U. A  C_ 
U. B

Proof of Theorem unissi
StepHypRef Expression
1 unissi.1 . 2  |-  A  C_  B
2 uniss 3727 . 2  |-  ( A 
C_  B  ->  U. A  C_ 
U. B )
31, 2ax-mp 5 1  |-  U. A  C_ 
U. B
Colors of variables: wff set class
Syntax hints:    C_ wss 3041   U.cuni 3706
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 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-tru 1319  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-v 2662  df-in 3047  df-ss 3054  df-uni 3707
This theorem is referenced by:  unidif  3738  unixpss  4622  tfrcllemssrecs  6217  tgvalex  12146  tgval2  12147  eltg4i  12151  ntrss2  12217  isopn3  12221
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