Theorem ssinss1 2237

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 2230	. 2 |- (A i^i B) (_ A
2		sstr2 2071	. 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 2046   (_ wss 2047

This theorem is referenced by:  tgclt 7624  distop 7649  fctopOLD 7650  cctop 7652  innei 7736  opnin 7869  lecm 9545  mdslj2 10247  mdslmd1lem1 10252  mdslmd1lem2 10253  inpws1 10455  qusp 10555

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-8 964  ax-10 966  ax-12 968  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-10o 1140  ax-16 1210  ax-11o 1218  ax-ext 1459

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 981  df-sb 1172  df-clab 1464  df-cleq 1469  df-clel 1472  df-v 1812  df-in 2051  df-ss 2053

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