Theorem ssbr 4092

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 4091	1 |- ( A C_ B -> ( C A D -> C B D ) )

Syntax hints:   -> wi 4   C_ wss 3168   class class class wbr 4048

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 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-11 1530  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559  ax-ext 2188

This theorem depends on definitions:  df-bi 117  df-nf 1485  df-sb 1787  df-clab 2193  df-cleq 2199  df-clel 2202  df-in 3174  df-ss 3181  df-br 4049

This theorem is referenced by:  ssrelrn  4875