Metamath Proof Explorer


Definition df-m1r

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. (Contributed by NM, 9-Aug-1995) (New usage is discouraged.)

Ref Expression
Assertion df-m1r -1R = [ ⟨ 1P , ( 1P +P 1P ) ⟩ ] ~R

Detailed syntax breakdown

Step Hyp Ref Expression
0 cm1r ⊢ -1R
1 c1p ⊢ 1P
2 cpp ⊢ +P
3 1 1 2 co ⊢ ( 1P +P 1P )
4 1 3 cop ⊢ ⟨ 1P , ( 1P +P 1P ) ⟩
5 cer ⊢ ~R
6 4 5 cec ⊢ [ ⟨ 1P , ( 1P +P 1P ) ⟩ ] ~R
7 0 6 wceq ⊢ -1R = [ ⟨ 1P , ( 1P +P 1P ) ⟩ ] ~R