Description: Subtracting a positive real from another number decreases it. (Contributed by Mario Carneiro, 28-May-2016)
Ref | Expression | ||
---|---|---|---|
Hypotheses | rpgecld.1 | |- ( ph -> A e. RR ) |
|
rpgecld.2 | |- ( ph -> B e. RR+ ) |
||
Assertion | ltsubrpd | |- ( ph -> ( A - B ) < A ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rpgecld.1 | |- ( ph -> A e. RR ) |
|
2 | rpgecld.2 | |- ( ph -> B e. RR+ ) |
|
3 | ltsubrp | |- ( ( A e. RR /\ B e. RR+ ) -> ( A - B ) < A ) |
|
4 | 1 2 3 | syl2anc | |- ( ph -> ( A - B ) < A ) |