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Theorem ssbr 4830
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 4829 1 (𝐴𝐵 → (𝐶𝐴𝐷𝐶𝐵𝐷))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wss 3723   class class class wbr 4786
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885  ax-5 1991  ax-6 2057  ax-7 2093  ax-9 2154  ax-10 2174  ax-11 2190  ax-12 2203  ax-ext 2751
This theorem depends on definitions:  df-bi 197  df-an 383  df-or 835  df-tru 1634  df-ex 1853  df-nf 1858  df-sb 2050  df-clab 2758  df-cleq 2764  df-clel 2767  df-in 3730  df-ss 3737  df-br 4787
This theorem is referenced by:  ssbri  4831  coss1  5416  coss2  5417  cnvss  5433  ssrelrn  5453  isucn2  22303  brelg  29759  cossss  34522
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