Description: Identity law for the shift operation. (Contributed by NM, 19-Aug-2005) (Revised by Mario Carneiro, 5-Nov-2013)
Ref | Expression | ||
---|---|---|---|
Hypothesis | shftfval.1 | |- F e. _V |
|
Assertion | shftidt | |- ( A e. CC -> ( ( F shift 0 ) ` A ) = ( F ` A ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | shftfval.1 | |- F e. _V |
|
2 | 1 | shftidt2 | |- ( F shift 0 ) = ( F |` CC ) |
3 | 2 | fveq1i | |- ( ( F shift 0 ) ` A ) = ( ( F |` CC ) ` A ) |
4 | fvres | |- ( A e. CC -> ( ( F |` CC ) ` A ) = ( F ` A ) ) |
|
5 | 3 4 | eqtrid | |- ( A e. CC -> ( ( F shift 0 ) ` A ) = ( F ` A ) ) |