Description: A member of the value of the partial isomorphism A is a translation, i.e., a vector. (Contributed by NM, 17-Jan-2014)
Ref | Expression | ||
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Hypotheses | diass.b | |- B = ( Base ` K ) |
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diass.l | |- .<_ = ( le ` K ) |
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diass.h | |- H = ( LHyp ` K ) |
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diass.t | |- T = ( ( LTrn ` K ) ` W ) |
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diass.i | |- I = ( ( DIsoA ` K ) ` W ) |
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Assertion | diael | |- ( ( ( K e. V /\ W e. H ) /\ ( X e. B /\ X .<_ W ) /\ F e. ( I ` X ) ) -> F e. T ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | diass.b | |- B = ( Base ` K ) |
|
2 | diass.l | |- .<_ = ( le ` K ) |
|
3 | diass.h | |- H = ( LHyp ` K ) |
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4 | diass.t | |- T = ( ( LTrn ` K ) ` W ) |
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5 | diass.i | |- I = ( ( DIsoA ` K ) ` W ) |
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6 | 1 2 3 4 5 | diass | |- ( ( ( K e. V /\ W e. H ) /\ ( X e. B /\ X .<_ W ) ) -> ( I ` X ) C_ T ) |
7 | 6 | sseld | |- ( ( ( K e. V /\ W e. H ) /\ ( X e. B /\ X .<_ W ) ) -> ( F e. ( I ` X ) -> F e. T ) ) |
8 | 7 | 3impia | |- ( ( ( K e. V /\ W e. H ) /\ ( X e. B /\ X .<_ W ) /\ F e. ( I ` X ) ) -> F e. T ) |