Theorem ssbr 4126

Description: Implication from a subclass relationship of binary relations. (Contributed by Peter Mazsa, 11-Nov-2019.)

Assertion

Ref	Expression
ssbr	|- ( A C_ B -> ( C A D -> C B D ) )

Proof of Theorem ssbr

Step	Hyp	Ref	Expression
1		id 19	. 2 |- ( A C_ B -> A C_ B )
2	1	ssbrd 4125	1 |- ( A C_ B -> ( C A D -> C B D ) )

Syntax hints:   -> wi 4   C_ wss 3197   class class class wbr 4082

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-11 1552  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211

This theorem depends on definitions:  df-bi 117  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-in 3203  df-ss 3210  df-br 4083

This theorem is referenced by:  ssrelrn  4913