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Theorem sslin 3481
 Description: Add left intersection to subclass relation. (Contributed by NM, 19-Oct-1999.)
Assertion
Ref Expression
sslin (A B → (CA) (CB))

Proof of Theorem sslin
StepHypRef Expression
1 ssrin 3480 . 2 (A B → (AC) (BC))
2 incom 3448 . 2 (CA) = (AC)
3 incom 3448 . 2 (CB) = (BC)
41, 2, 33sstr4g 3312 1 (A B → (CA) (CB))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∩ cin 3208   ⊆ wss 3257 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-ss 3259 This theorem is referenced by:  ss2in  3482  ssres2  4991  ssrnres  5059  sbthlem1  6203
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