Description: The composition of continuous functions is continuous. (Contributed by Mario Carneiro, 5-May-2014) (Revised by Mario Carneiro, 22-Aug-2015)
Ref | Expression | ||
---|---|---|---|
Hypotheses | cnmptid.j | |
|
cnmpt11.a | |
||
cnmpt11f.f | |
||
Assertion | cnmpt11f | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cnmptid.j | |
|
2 | cnmpt11.a | |
|
3 | cnmpt11f.f | |
|
4 | cntop2 | |
|
5 | 2 4 | syl | |
6 | toptopon2 | |
|
7 | 5 6 | sylib | |
8 | eqid | |
|
9 | eqid | |
|
10 | 8 9 | cnf | |
11 | 3 10 | syl | |
12 | 11 | feqmptd | |
13 | 12 3 | eqeltrrd | |
14 | fveq2 | |
|
15 | 1 2 7 13 14 | cnmpt11 | |