Description: Lemma for Proposition 9-3.5(iv) of Gleason p. 123. (Contributed by NM, 3-Apr-1996) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Hypothesis | ltexprlem.1 | |
|
Assertion | ltexprlem2 | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ltexprlem.1 | |
|
2 | 1 | abeq2i | |
3 | elprnq | |
|
4 | addnqf | |
|
5 | 4 | fdmi | |
6 | 0nnq | |
|
7 | 5 6 | ndmovrcl | |
8 | 3 7 | syl | |
9 | ltaddnq | |
|
10 | 9 | ancoms | |
11 | addcomnq | |
|
12 | 10 11 | breqtrdi | |
13 | prcdnq | |
|
14 | 12 13 | syl5 | |
15 | 8 14 | mpd | |
16 | 15 | ex | |
17 | 16 | adantld | |
18 | 17 | exlimdv | |
19 | 2 18 | syl5bi | |
20 | 19 | ssrdv | |
21 | prpssnq | |
|
22 | 20 21 | sspsstrd | |