Description: Reverse closure of a lattice automorphism. (Contributed by NM, 25-May-2012) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Hypotheses | laut1o.b | |- B = ( Base ` K ) |
|
laut1o.i | |- I = ( LAut ` K ) |
||
Assertion | lautcnvclN | |- ( ( ( 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 | f1ocnvdm | |- ( ( F : B -1-1-onto-> B /\ X e. B ) -> ( `' F ` X ) e. B ) |
|
5 | 3 4 | sylan | |- ( ( ( K e. V /\ F e. I ) /\ X e. B ) -> ( `' F ` X ) e. B ) |