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Theorem sseq12 4004
Description: Equality theorem for the subclass relationship. (Contributed by NM, 31-May-1999.)
Assertion
Ref Expression
sseq12 ((𝐴 = 𝐵𝐶 = 𝐷) → (𝐴𝐶𝐵𝐷))

Proof of Theorem sseq12
StepHypRef Expression
1 sseq1 4002 . 2 (𝐴 = 𝐵 → (𝐴𝐶𝐵𝐶))
2 sseq2 4003 . 2 (𝐶 = 𝐷 → (𝐵𝐶𝐵𝐷))
31, 2sylan9bb 509 1 ((𝐴 = 𝐵𝐶 = 𝐷) → (𝐴𝐶𝐵𝐷))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 205  wa 395   = wceq 1533  wss 3943
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2697
This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1536  df-ex 1774  df-sb 2060  df-clab 2704  df-cleq 2718  df-clel 2804  df-v 3470  df-in 3950  df-ss 3960
This theorem is referenced by:  sseq12i  4007  sorpsscmpl  7720  funcnvuni  7918  fiunlem  7924  sornom  10271  axdc3lem2  10445  ipole  18497  ipodrsima  18504  metsscmetcld  25194  funpsstri  35270  brredunds  38007  ismrcd2  41996  ismrc  41998
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