Description: A lattice automorphism value belongs to the base set. (Contributed by NM, 20-May-2012)
Ref | Expression | ||
---|---|---|---|
Hypotheses | laut1o.b | |- B = ( Base ` K ) |
|
laut1o.i | |- I = ( LAut ` K ) |
||
Assertion | lautcl | |- ( ( ( K e. V /\ F e. I ) /\ X e. B ) -> ( F ` X ) e. B ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | laut1o.b | |- B = ( Base ` K ) |
|
2 | laut1o.i | |- I = ( LAut ` K ) |
|
3 | 1 2 | laut1o | |- ( ( K e. V /\ F e. I ) -> F : B -1-1-onto-> B ) |
4 | f1of | |- ( F : B -1-1-onto-> B -> F : B --> B ) |
|
5 | 3 4 | syl | |- ( ( K e. V /\ F e. I ) -> F : B --> B ) |
6 | 5 | ffvelrnda | |- ( ( ( K e. V /\ F e. I ) /\ X e. B ) -> ( F ` X ) e. B ) |