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Metamath Proof Explorer

Definition df-0r

Description: Define signed real constant 0. This is a "temporary" set used in the construction of complex numbers df-c , and is intended to be used only by the construction. From Proposition 9-4.2 of Gleason p. 126. (Contributed by NM, 9-Aug-1995) (New usage is discouraged.)

Ref Expression
Assertion df-0r 0R = [ ⟨ 1P , 1P ⟩ ] ~R

Detailed syntax breakdown

Step Hyp Ref Expression
0 c0r ⊢ 0R
1 c1p ⊢ 1P
2 1 1 cop ⊢ ⟨ 1P , 1P ⟩
3 cer ⊢ ~R
4 2 3 cec ⊢ [ ⟨ 1P , 1P ⟩ ] ~R
5 0 4 wceq ⊢ 0R = [ ⟨ 1P , 1P ⟩ ] ~R