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Theorem ssbr 5197
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 5196 1 (𝐴𝐵 → (𝐶𝐴𝐷𝐶𝐵𝐷))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wss 3947   class class class wbr 5153
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101
This theorem depends on definitions:  df-bi 206  df-an 395  df-ex 1775  df-clel 2803  df-ss 3964  df-br 5154
This theorem is referenced by:  ssbri  5198  coss1  5862  coss2  5863  cnvss  5879  ssrelrn  5901  ttrclss  9763  isucn2  24275  brelg  32529  cossss  38123
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