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Theorem ssel2 3268
 Description: Membership relationships follow from a subclass relationship. (Contributed by NM, 7-Jun-2004.)
Assertion
Ref Expression
ssel2 ((A B C A) → C B)

Proof of Theorem ssel2
StepHypRef Expression
1 ssel 3267 . 2 (A B → (C AC B))
21imp 418 1 ((A B C A) → C B)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 358   ∈ wcel 1710   ⊆ wss 3257 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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:  phialllem1  4616  fcnvres  5243  dfimafn  5366  funimass4  5368  funfvima3  5461  isomin  5496  enprmaplem5  6080
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