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Theorem ssbri 3847
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 3846 . 2 (⊤ → (𝐶𝐴𝐷𝐶𝐵𝐷))
43trud 1294 1 (𝐶𝐴𝐷𝐶𝐵𝐷)
Colors of variables: wff set class
Syntax hints:  wi 4  wtru 1286  wss 2982   class class class wbr 3805
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 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-11 1438  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-in 2988  df-ss 2995  df-br 3806
This theorem is referenced by:  brel  4438  swoer  6222  swoord1  6223  swoord2  6224  ecopover  6292  ecopoverg  6295  endom  6332
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