Theorem ssinss1 2240

Description: Intersection preserves subclass relationship.

Assertion

Ref	Expression
ssinss1	|- (A (_ C -> (A i^i B) (_ C)

Proof of Theorem ssinss1

Step	Hyp	Ref	Expression
1		inss1 2233	. 2 |- (A i^i B) (_ A
2		sstr2 2074	. 2 |- ((A i^i B) (_ A -> (A (_ C -> (A i^i B) (_ C))
3	1, 2	ax-mp 7	1 |- (A (_ C -> (A i^i B) (_ C)

Syntax hints:   -> wi 3   i^i cin 2049   (_ wss 2050

This theorem is referenced by:  tgclt 7623  distop 7646  fctopOLD 7647  cctop 7649  innei 7733  opnin 7866  lecm 9540  mdslj2 10242  mdslmd1lem1 10247  mdslmd1lem2 10248  inpws1 10445  qusp 10541

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 964  ax-gen 965  ax-8 966  ax-10 968  ax-12 970  ax-17 973  ax-4 975  ax-5o 977  ax-6o 980  ax-9o 1125  ax-10o 1142  ax-16 1212  ax-11o 1220  ax-ext 1462

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 983  df-sb 1174  df-clab 1467  df-cleq 1472  df-clel 1475  df-v 1815  df-in 2054  df-ss 2056

Copyright terms: Public domain