Description: Sufficient condition for a restricted converse epsilon coset to be a set. (Contributed by Peter Mazsa, 24-Sep-2021)
Ref | Expression | ||
---|---|---|---|
Assertion | 1cosscnvepresex | |- ( A e. V -> ,~ ( `' _E |` A ) e. _V ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cnvepresex | |- ( A e. V -> ( `' _E |` A ) e. _V ) |
|
2 | cossex | |- ( ( `' _E |` A ) e. _V -> ,~ ( `' _E |` A ) e. _V ) |
|
3 | 1 2 | syl | |- ( A e. V -> ,~ ( `' _E |` A ) e. _V ) |