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

Theorem ssbri 3879
Description: Inference from a subclass relationship of binary relations. (Contributed by NM, 28-Mar-2007.) (Revised by Mario Carneiro, 8-Feb-2015.)
Hypothesis
Ref Expression
ssbri.1  |-  A  C_  B
Assertion
Ref Expression
ssbri  |-  ( C A D  ->  C B D )

Proof of Theorem ssbri
StepHypRef Expression
1 ssbri.1 . . . 4  |-  A  C_  B
21a1i 9 . . 3  |-  ( T. 
->  A  C_  B )
32ssbrd 3878 . 2  |-  ( T. 
->  ( C A D  ->  C B D ) )
43mptru 1298 1  |-  ( C A D  ->  C B D )
Colors of variables: wff set class
Syntax hints:    -> wi 4   T. wtru 1290    C_ wss 2997   class class class wbr 3837
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-11 1442  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-in 3003  df-ss 3010  df-br 3838
This theorem is referenced by:  brel  4478  swoer  6300  swoord1  6301  swoord2  6302  ecopover  6370  ecopoverg  6373  endom  6460
  Copyright terms: Public domain W3C validator