Description: An indexed intersection of elements of C is an element of the finite intersections of C . (Contributed by Mario Carneiro, 30-Aug-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | iinfi | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpr1 | |
|
2 | dfiin2g | |
|
3 | 1 2 | syl | |
4 | eqid | |
|
5 | 4 | rnmpt | |
6 | 5 | inteqi | |
7 | 3 6 | eqtr4di | |
8 | 4 | fmpt | |
9 | 8 | 3anbi1i | |
10 | intrnfi | |
|
11 | 9 10 | sylan2b | |
12 | 7 11 | eqeltrd | |