Theorem fnoa 3117

Description: Functionality and domain of ordinal addition.

Assertion

Ref	Expression
fnoa	⊢ +o Fn (On × On)

Proof of Theorem fnoa

Step	Hyp	Ref	Expression
1		fvex 2838	. 2 ⊢ (rec({⟨w, v⟩∣v = suc w}, x) ‘y) ∈ V
2		df-oadd 3106	. 2 ⊢ +o = {⟨⟨x, y⟩, z⟩∣((x ∈ On ∧ y ∈ On) ∧ z = (rec({⟨w, v⟩∣v = suc w}, x) ‘y))}
3	1, 2	fnoprab2 3039	1 ⊢ +o Fn (On × On)

Syntax hints:   = wceq 1091  {copab 2055  Oncon0 2199  suc csuc 2201   × cxp 2408   Fn wfn 2417   ‘cfv 2422  reccrdg 2969   +_o coa 3101

This theorem is referenced by:  dmaddpi 3812

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-7 676  ax-gen 677  ax-8 798  ax-9 799  ax-10 800  ax-11 801  ax-12 802  ax-13 804  ax-14 805  ax-16 922  ax-17 925  ax-ext 1074  ax-rep 1075  ax-un 1076  ax-pow 1077

This theorem depends on definitions:  df-bi 128  df-or 197  df-an 198  df-ex 679  df-sb 853  df-eu 1009  df-mo 1010  df-clab 1093  df-cleq 1097  df-clel 1099  df-v 1349  df-dif 1489  df-un 1490  df-in 1491  df-ss 1492  df-nul 1708  df-pw 1799  df-sn 1811  df-pr 1812  df-op 1815  df-uni 1920  df-br 2063  df-opab 2098  df-id 2125  df-xp 2424  df-rel 2425  df-cnv 2426  df-co 2427  df-dm 2428  df-fun 2432  df-fn 2433  df-fv 2438  df-oprab 3004  df-oadd 3106

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