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