Theorem ssbri 4077

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 4076	. 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 3157   class class class wbr 4033

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 1461  ax-7 1462  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-8 1518  ax-11 1520  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548  ax-i5r 1549  ax-ext 2178

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1475  df-sb 1777  df-clab 2183  df-cleq 2189  df-clel 2192  df-in 3163  df-ss 3170  df-br 4034

This theorem is referenced by:  brel  4715  swoer  6620  swoord1  6621  swoord2  6622  ecopover  6692  ecopoverg  6695  endom  6822