Step |
Hyp |
Ref |
Expression |
1 |
|
iccmbl |
|- ( ( A e. RR /\ B e. RR ) -> ( A [,] B ) e. dom vol ) |
2 |
|
mblvol |
|- ( ( A [,] B ) e. dom vol -> ( vol ` ( A [,] B ) ) = ( vol* ` ( A [,] B ) ) ) |
3 |
1 2
|
syl |
|- ( ( A e. RR /\ B e. RR ) -> ( vol ` ( A [,] B ) ) = ( vol* ` ( A [,] B ) ) ) |
4 |
3
|
3adant3 |
|- ( ( A e. RR /\ B e. RR /\ A <_ B ) -> ( vol ` ( A [,] B ) ) = ( vol* ` ( A [,] B ) ) ) |
5 |
|
ovolicc |
|- ( ( A e. RR /\ B e. RR /\ A <_ B ) -> ( vol* ` ( A [,] B ) ) = ( B - A ) ) |
6 |
4 5
|
eqtrd |
|- ( ( A e. RR /\ B e. RR /\ A <_ B ) -> ( vol ` ( A [,] B ) ) = ( B - A ) ) |