Description: Addition of positive fractions in terms of positive integers. (Contributed by NM, 28-Aug-1995) (Revised by Mario Carneiro, 26-Dec-2014) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Assertion | addpqnq | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-plq | |
|
2 | 1 | fveq1i | |
3 | 2 | a1i | |
4 | opelxpi | |
|
5 | 4 | fvresd | |
6 | df-plpq | |
|
7 | opex | |
|
8 | 6 7 | fnmpoi | |
9 | elpqn | |
|
10 | elpqn | |
|
11 | opelxpi | |
|
12 | 9 10 11 | syl2an | |
13 | fvco2 | |
|
14 | 8 12 13 | sylancr | |
15 | 3 5 14 | 3eqtrd | |
16 | df-ov | |
|
17 | df-ov | |
|
18 | 17 | fveq2i | |
19 | 15 16 18 | 3eqtr4g | |