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Theorem sseq12 4023
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 4021 . 2 (𝐴 = 𝐵 → (𝐴𝐶𝐵𝐶))
2 sseq2 4022 . 2 (𝐶 = 𝐷 → (𝐵𝐶𝐵𝐷))
31, 2sylan9bb 509 1 ((𝐴 = 𝐵𝐶 = 𝐷) → (𝐴𝐶𝐵𝐷))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 206  wa 395   = wceq 1537  wss 3963
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-9 2116  ax-ext 2706
This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1777  df-cleq 2727  df-ss 3980
This theorem is referenced by:  sseq12i  4026  sorpsscmpl  7753  funcnvuni  7955  fiunlem  7965  sornom  10315  axdc3lem2  10489  ipole  18592  ipodrsima  18599  metsscmetcld  25363  funpsstri  35747  brredunds  38608  ismrcd2  42687  ismrc  42689
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