Description: A family of subgroups indexed by a proper class cannot be a family of subgroups for an internal direct product. (Contributed by AV, 13-Jul-2019)
Ref | Expression | ||
---|---|---|---|
Assertion | dprddomprc |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-nel | ||
2 | dmexg | ||
3 | 2 | con3i | |
4 | 1 3 | sylbi | |
5 | reldmdprd | ||
6 | 5 | brrelex2i | |
7 | 4 6 | nsyl |