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Theorem ssbr 5191
Description: Implication from a subclass relationship of binary relations. (Contributed by Peter Mazsa, 11-Nov-2019.)
Assertion
Ref Expression
ssbr (𝐴𝐵 → (𝐶𝐴𝐷𝐶𝐵𝐷))

Proof of Theorem ssbr
StepHypRef Expression
1 id 22 . 2 (𝐴𝐵𝐴𝐵)
21ssbrd 5190 1 (𝐴𝐵 → (𝐶𝐴𝐷𝐶𝐵𝐷))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wss 3947   class class class wbr 5147
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2703
This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1544  df-ex 1782  df-sb 2068  df-clab 2710  df-cleq 2724  df-clel 2810  df-v 3476  df-in 3954  df-ss 3964  df-br 5148
This theorem is referenced by:  ssbri  5192  coss1  5853  coss2  5854  cnvss  5870  ssrelrn  5892  ttrclss  9711  isucn2  23775  brelg  31825  cossss  37283
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