Theorem ssdifss 2168

Description: Preservation of a subclass relationship by class difference.

Assertion

Ref	Expression
ssdifss	|- (A (_ B -> (A \ C) (_ B)

Proof of Theorem ssdifss

Step	Hyp	Ref	Expression
1		difss 2167	. 2 |- (A \ C) (_ A
2		sstr 2072	. 2 |- (((A \ C) (_ A /\ A (_ B) -> (A \ C) (_ B)
3	1, 2	mpan 695	1 |- (A (_ B -> (A \ C) (_ B)

Syntax hints:   -> wi 3   \ cdif 2044   (_ wss 2047

This theorem is referenced by:  unblem1 4540  xrsupss 6078  xrinfmss 6079  islp2 7747  rcfpfillem6 10595  rcfpfillem6OLD 10596

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-dif 2049  df-in 2051  df-ss 2053

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