Description: A positive real has no largest member. Addition version. (Contributed by NM, 7-Apr-1996) (Revised by Mario Carneiro, 11-May-2013) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Assertion | prnmadd | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | prnmax | |
|
2 | ltrelnq | |
|
3 | 2 | brel | |
4 | 3 | simprd | |
5 | ltexnq | |
|
6 | 5 | biimpcd | |
7 | 4 6 | mpd | |
8 | eleq1a | |
|
9 | 8 | eximdv | |
10 | 7 9 | syl5 | |
11 | 10 | rexlimiv | |
12 | 1 11 | syl | |