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 |
| 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 |