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 |
| 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 |