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Theorem sseq12 3294
 Description: Equality theorem for the subclass relationship. (Contributed by NM, 31-May-1999.)
Assertion
Ref Expression
sseq12 ((A = B C = D) → (A CB D))

Proof of Theorem sseq12
StepHypRef Expression
1 sseq1 3292 . 2 (A = B → (A CB C))
2 sseq2 3293 . 2 (C = D → (B CB D))
31, 2sylan9bb 680 1 ((A = B C = D) → (A CB D))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176   ∧ wa 358   = wceq 1642   ⊆ 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:  sseq12i  3297  ssfin  4470  funcnvuni  5161  fun11iun  5305
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