Description: Equality implies 'less than or equal to'. (Contributed by Glauco Siliprandi, 17-Aug-2020)
Ref | Expression | ||
---|---|---|---|
Hypotheses | xreqled.1 | |- ( ph -> A e. RR* ) |
|
xreqled.2 | |- ( ph -> A = B ) |
||
Assertion | xreqled | |- ( ph -> A <_ B ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | xreqled.1 | |- ( ph -> A e. RR* ) |
|
2 | xreqled.2 | |- ( ph -> A = B ) |
|
3 | xreqle | |- ( ( A e. RR* /\ A = B ) -> A <_ B ) |
|
4 | 1 2 3 | syl2anc | |- ( ph -> A <_ B ) |