Theorem ssdifss 2158

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 2157	. 2 |- (A \ C) (_ A
2		sstr 2062	. 2 |- (((A \ C) (_ A /\ A (_ B) -> (A \ C) (_ B)
3	1, 2	mpan 693	1 |- (A (_ B -> (A \ C) (_ B)

Syntax hints:   -> wi 3   \ cdif 2034   (_ wss 2037

This theorem is referenced by:  unblem1 4517  xrsupss 6025  xrinfmss 6026  islp2 7688

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 959  ax-gen 960  ax-8 961  ax-10 963  ax-12 965  ax-17 968  ax-4 970  ax-5o 972  ax-6o 975  ax-9o 1119  ax-10o 1136  ax-16 1206  ax-11o 1213  ax-ext 1452

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 978  df-sb 1168  df-clab 1457  df-cleq 1462  df-clel 1465  df-v 1803  df-dif 2039  df-in 2041  df-ss 2043

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