Theorem ssbri 2657

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 1475	. 2 |- A = A
2		ssbri.1	. . . 4 |- A (_ B
3	2	a1i 8	. . 3 |- (A = A -> A (_ B)
4	3	ssbrd 2656	. 2 |- (A = A -> (CAD -> CBD))
5	1, 4	ax-mp 7	1 |- (CAD -> CBD)

Syntax hints:   -> wi 3   = wceq 956   (_ wss 2047   class class class wbr 2619

This theorem is referenced by:  endom 4385  brdom3 4801  brdom5 4802  brdom4 4803

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-8 964  ax-10 966  ax-12 968  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-10o 1140  ax-16 1210  ax-11o 1218  ax-ext 1459

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 981  df-sb 1172  df-clab 1464  df-cleq 1469  df-clel 1472  df-in 2051  df-ss 2053  df-br 2620

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