Metamath Proof Explorer


Theorem diael

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
Hypotheses diass.b B = Base K
diass.l ˙ = K
diass.h H = LHyp K
diass.t T = LTrn K W
diass.i I = DIsoA K W
Assertion diael K V W H X B X ˙ W F I X F T

Proof

Step Hyp Ref Expression
1 diass.b B = Base K
2 diass.l ˙ = K
3 diass.h H = LHyp K
4 diass.t T = LTrn K W
5 diass.i I = DIsoA K W
6 1 2 3 4 5 diass K V W H X B X ˙ W I X T
7 6 sseld K V W H X B X ˙ W F I X F T
8 7 3impia K V W H X B X ˙ W F I X F T