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Theorem ssbri 3797
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 AB
Assertion
Ref Expression
ssbri (𝐶A𝐷𝐶B𝐷)

Proof of Theorem ssbri
StepHypRef Expression
1 ssbri.1 . . . 4 AB
21a1i 9 . . 3 ( ⊤ → AB)
32ssbrd 3796 . 2 ( ⊤ → (𝐶A𝐷𝐶B𝐷))
43trud 1251 1 (𝐶A𝐷𝐶B𝐷)
Colors of variables: wff set class
Syntax hints:  wi 4  wtru 1243  wss 2911   class class class wbr 3755
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-in 2918  df-ss 2925  df-br 3756
This theorem is referenced by:  brel  4335  swoer  6070  swoord1  6071  swoord2  6072  ecopover  6140  ecopoverg  6143  endom  6179
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