Theorem ssbri 4133

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 4131	. 2 |- ( T. -> ( C A D -> C B D ) )
4	3	mptru 1406	1 |- ( C A D -> C B D )

Syntax hints:   -> wi 4   T. wtru 1398   C_ wss 3200   class class class wbr 4088

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 1495  ax-7 1496  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-11 1554  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582  ax-i5r 1583  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-tru 1400  df-nf 1509  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-in 3206  df-ss 3213  df-br 4089

This theorem is referenced by:  brel  4778  swoer  6729  swoord1  6730  swoord2  6731  ecopover  6801  ecopoverg  6804  endom  6935