Theorem ssbri 2647

Description: Inference from a subclass relationship of binary relations.

Hypothesis

Ref	Expression
ssbri.1	|- A (_ B

Assertion

Ref	Expression
ssbri	|- (CAD -> CBD)

Proof of Theorem ssbri

Step	Hyp	Ref	Expression
1		eqid 1468	. 2 |- A = A
2		ssbri.1	. . . 4 |- A (_ B
3	2	a1i 8	. . 3 |- (A = A -> A (_ B)
4	3	ssbrd 2646	. 2 |- (A = A -> (CAD -> CBD))
5	1, 4	ax-mp 7	1 |- (CAD -> CBD)

Syntax hints:   -> wi 3   = wceq 953   (_ wss 2037   class class class wbr 2609

This theorem is referenced by:  endom 4366  brdom3 4773  brdom5 4774  brdom4 4775

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 959  ax-gen 960  ax-8 961  ax-10 963  ax-12 965  ax-17 968  ax-4 970  ax-5o 972  ax-6o 975  ax-9o 1119  ax-10o 1136  ax-16 1206  ax-11o 1213  ax-ext 1452

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 978  df-sb 1168  df-clab 1457  df-cleq 1462  df-clel 1465  df-in 2041  df-ss 2043  df-br 2610

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