Theorem sslin 2238

Description: Add left intersection to subclass relation.

Assertion

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

Proof of Theorem sslin

Step	Hyp	Ref	Expression
1		ssrin 2237	. 2 |- (A (_ B -> (A i^i C) (_ (B i^i C))
2		incom 2211	. 2 |- (C i^i A) = (A i^i C)
3		incom 2211	. 2 |- (C i^i B) = (B i^i C)
4	1, 2, 3	3sstr4g 2105	1 |- (A (_ B -> (C i^i A) (_ (C i^i B))

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

This theorem is referenced by:  ss2in 2239  ssres2 3392  ssrnres 3487  sbthlem7 4459  kmlem5 4779  infxpidmlem11 7563  sncld 7784  lpbl 7877  chssoct 9414  cmbr4 9539  5oa 9601  3oalem6 9607  mdslmd4 10255  atcvat4 10319

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

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