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Theorem ssbri 3940
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 3939 . 2  |-  ( T. 
->  ( C A D  ->  C B D ) )
43mptru 1323 1  |-  ( C A D  ->  C B D )
Colors of variables: wff set class
Syntax hints:    -> wi 4   T. wtru 1315    C_ wss 3039   class class class wbr 3897
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-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-11 1467  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097
This theorem depends on definitions:  df-bi 116  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-in 3045  df-ss 3052  df-br 3898
This theorem is referenced by:  brel  4559  swoer  6423  swoord1  6424  swoord2  6425  ecopover  6493  ecopoverg  6496  endom  6623
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