Theorem ssbri 3972

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 3971	. 2 |- ( T. -> ( C A D -> C B D ) )
4	3	mptru 1340	1 |- ( C A D -> C B D )

Syntax hints:   -> wi 4   T. wtru 1332   C_ wss 3071   class class class wbr 3929

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-11 1484  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121

This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-in 3077  df-ss 3084  df-br 3930

This theorem is referenced by:  brel  4591  swoer  6457  swoord1  6458  swoord2  6459  ecopover  6527  ecopoverg  6530  endom  6657