Description: Multiplication of both sides of 'less than' by a positive number. Theorem I.19 of Apostol p. 20. (Contributed by NM, 16-May-1999)
Ref | Expression | ||
---|---|---|---|
Hypotheses | ltplus1.1 | |
|
prodgt0.2 | |
||
ltmul1.3 | |
||
Assertion | ltmul2i | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ltplus1.1 | |
|
2 | prodgt0.2 | |
|
3 | ltmul1.3 | |
|
4 | ltmul2 | |
|
5 | 1 2 4 | mp3an12 | |
6 | 3 5 | mpan | |