Description: Multiplication of both sides of 'less than or equal to' by a nonnegative number. (Contributed by Paul Chapman, 7-Sep-2007)
Ref | Expression | ||
---|---|---|---|
Assertion | lemul2a | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | lemul1a | |
|
2 | recn | |
|
3 | recn | |
|
4 | mulcom | |
|
5 | 2 3 4 | syl2an | |
6 | 5 | adantrr | |
7 | 6 | 3adant2 | |
8 | 7 | adantr | |
9 | recn | |
|
10 | mulcom | |
|
11 | 9 3 10 | syl2an | |
12 | 11 | adantrr | |
13 | 12 | 3adant1 | |
14 | 13 | adantr | |
15 | 1 8 14 | 3brtr3d | |