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Theorem ssbr 4888
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 4887 1 (𝐴𝐵 → (𝐶𝐴𝐷𝐶𝐵𝐷))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wss 3769   class class class wbr 4844
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1877  ax-4 1894  ax-5 2001  ax-6 2068  ax-7 2104  ax-9 2165  ax-10 2185  ax-11 2201  ax-12 2214  ax-ext 2784
This theorem depends on definitions:  df-bi 198  df-an 385  df-or 866  df-tru 1641  df-ex 1860  df-nf 1864  df-sb 2061  df-clab 2793  df-cleq 2799  df-clel 2802  df-in 3776  df-ss 3783  df-br 4845
This theorem is referenced by:  ssbri  4889  coss1  5479  coss2  5480  cnvss  5496  ssrelrn  5516  isucn2  22293  brelg  29745  cossss  34491
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