ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  unissi Unicode version

Theorem unissi 3817
Description: Subclass relationship for subclass union. Inference form of uniss 3815. (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 3815 . 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 3121   U.cuni 3794
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 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152
This theorem depends on definitions:  df-bi 116  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-v 2732  df-in 3127  df-ss 3134  df-uni 3795
This theorem is referenced by:  unidif  3826  unixpss  4722  tfrcllemssrecs  6328  tgvalex  12765  tgval2  12766  eltg4i  12770  ntrss2  12836  isopn3  12840
  Copyright terms: Public domain W3C validator