Theorem ssbri 4073

Description: Inference from a subclass relationship of binary relations. (Contributed by NM, 28-Mar-2007.) (Revised by Mario Carneiro, 8-Feb-2015.)

Hypothesis

Ref	Expression
ssbri.1	|- A C_ B

Assertion

Ref	Expression
ssbri	|- ( C A D -> C B D )

Proof of Theorem ssbri

Step	Hyp	Ref	Expression
1		ssbri.1	. . . 4 |- A C_ B
2	1	a1i 9	. . 3 |- ( T. -> A C_ B )
3	2	ssbrd 4072	. 2 |- ( T. -> ( C A D -> C B D ) )
4	3	mptru 1373	1 |- ( C A D -> C B D )

Syntax hints:   -> wi 4   T. wtru 1365   C_ wss 3153   class class class wbr 4029

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 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-11 1517  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2175

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-in 3159  df-ss 3166  df-br 4030

This theorem is referenced by:  brel  4711  swoer  6615  swoord1  6616  swoord2  6617  ecopover  6687  ecopoverg  6690  endom  6817