Description: Define class of signed reals. 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, 25-Jul-1995) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | df-nr | |- R. = ( ( P. X. P. ) /. ~R ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 0 | cnr | |- R. |
|
| 1 | cnp | |- P. |
|
| 2 | 1 1 | cxp | |- ( P. X. P. ) |
| 3 | cer | |- ~R |
|
| 4 | 2 3 | cqs | |- ( ( P. X. P. ) /. ~R ) |
| 5 | 0 4 | wceq | |- R. = ( ( P. X. P. ) /. ~R ) |