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Metamath Proof Explorer

Definition df-1r

Description: Define signed real constant 1. 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-1r 1R = [ ⟨ ( 1P +P 1P ) , 1P ⟩ ] ~R

Detailed syntax breakdown

Step Hyp Ref Expression
0 c1r ⊢ 1R
1 c1p ⊢ 1P
2 cpp ⊢ +P
3 1 1 2 co ⊢ ( 1P +P 1P )
4 3 1 cop ⊢ ⟨ ( 1P +P 1P ) , 1P ⟩
5 cer ⊢ ~R
6 4 5 cec ⊢ [ ⟨ ( 1P +P 1P ) , 1P ⟩ ] ~R
7 0 6 wceq ⊢ 1R = [ ⟨ ( 1P +P 1P ) , 1P ⟩ ] ~R