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Theorem sseq12 3661
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 3659 . 2 (𝐴 = 𝐵 → (𝐴𝐶𝐵𝐶))
2 sseq2 3660 . 2 (𝐶 = 𝐷 → (𝐵𝐶𝐵𝐷))
31, 2sylan9bb 736 1 ((𝐴 = 𝐵𝐶 = 𝐷) → (𝐴𝐶𝐵𝐷))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  wa 383   = wceq 1523  wss 3607
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-9 2039  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282  ax-ext 2631
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1526  df-ex 1745  df-nf 1750  df-sb 1938  df-clab 2638  df-cleq 2644  df-clel 2647  df-in 3614  df-ss 3621
This theorem is referenced by:  sseq12i  3664  sorpsscmpl  6990  funcnvuni  7161  fun11iun  7168  sornom  9137  axdc3lem2  9311  ipole  17205  ipodrsima  17212  cmetss  23159  funpsstri  31789  ismrcd2  37579  ismrc  37581
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