Description: Express the predicate " <. X , D >. is an extended metric space" with underlying set X and distance function D . (Contributed by Mario Carneiro, 2-Sep-2015)
Ref | Expression | ||
---|---|---|---|
Hypotheses | isms.j | |
|
isms.x | |
||
isms.d | |
||
Assertion | isxms | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | isms.j | |
|
2 | isms.x | |
|
3 | isms.d | |
|
4 | fveq2 | |
|
5 | 4 1 | eqtr4di | |
6 | fveq2 | |
|
7 | fveq2 | |
|
8 | 7 2 | eqtr4di | |
9 | 8 | sqxpeqd | |
10 | 6 9 | reseq12d | |
11 | 10 3 | eqtr4di | |
12 | 11 | fveq2d | |
13 | 5 12 | eqeq12d | |
14 | df-xms | |
|
15 | 13 14 | elrab2 | |