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Theorem reldmopsr 19796
 Description: Lemma for ordered power series. (Contributed by Stefan O'Rear, 2-Oct-2015.)
Assertion
Ref Expression
reldmopsr Rel dom ordPwSer

Proof of Theorem reldmopsr
Dummy variables 𝑟 𝑖 𝑝 𝑠 𝑑 𝑤 𝑥 𝑦 𝑧 are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-opsr 19683 . 2 ordPwSer = (𝑖 ∈ V, 𝑠 ∈ V ↦ (𝑟 ∈ 𝒫 (𝑖 × 𝑖) ↦ (𝑖 mPwSer 𝑠) / 𝑝(𝑝 sSet ⟨(le‘ndx), {⟨𝑥, 𝑦⟩ ∣ ({𝑥, 𝑦} ⊆ (Base‘𝑝) ∧ ([{ ∈ (ℕ0𝑚 𝑖) ∣ ( “ ℕ) ∈ Fin} / 𝑑]𝑧𝑑 ((𝑥𝑧)(lt‘𝑠)(𝑦𝑧) ∧ ∀𝑤𝑑 (𝑤(𝑟 <bag 𝑖)𝑧 → (𝑥𝑤) = (𝑦𝑤))) ∨ 𝑥 = 𝑦))}⟩)))
21reldmmpt2 7005 1 Rel dom ordPwSer
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 385   ∨ wo 874   = wceq 1653   ∈ wcel 2157  ∀wral 3089  ∃wrex 3090  {crab 3093  Vcvv 3385  [wsbc 3633  ⦋csb 3728   ⊆ wss 3769  𝒫 cpw 4349  {cpr 4370  ⟨cop 4374   class class class wbr 4843  {copab 4905   ↦ cmpt 4922   × cxp 5310  ◡ccnv 5311  dom cdm 5312   “ cima 5315  Rel wrel 5317  ‘cfv 6101  (class class class)co 6878   ↑𝑚 cmap 8095  Fincfn 8195  ℕcn 11312  ℕ0cn0 11580  ndxcnx 16181   sSet csts 16182  Basecbs 16184  lecple 16274  ltcplt 17256   mPwSer cmps 19674
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