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Theorem ssinss1 3483
 Description: Intersection preserves subclass relationship. (Contributed by NM, 14-Sep-1999.)
Assertion
Ref Expression
ssinss1 (A C → (AB) C)

Proof of Theorem ssinss1
StepHypRef Expression
1 inss1 3475 . 2 (AB) A
2 sstr2 3279 . 2 ((AB) A → (A C → (AB) C))
31, 2ax-mp 8 1 (A C → (AB) C)
 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:  inss  3484
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