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