Metamath Proof Explorer


Theorem 5tcu2e40

Description: 5 times the cube of 2 is 40. (Contributed by AV, 4-Jul-2020)

Ref Expression
Assertion 5tcu2e40
|- ( 5 x. ( 2 ^ 3 ) ) = ; 4 0

Proof

Step Hyp Ref Expression
1 cu2
 |-  ( 2 ^ 3 ) = 8
2 1 oveq2i
 |-  ( 5 x. ( 2 ^ 3 ) ) = ( 5 x. 8 )
3 5cn
 |-  5 e. CC
4 8cn
 |-  8 e. CC
5 3 4 mulcomi
 |-  ( 5 x. 8 ) = ( 8 x. 5 )
6 8t5e40
 |-  ( 8 x. 5 ) = ; 4 0
7 2 5 6 3eqtri
 |-  ( 5 x. ( 2 ^ 3 ) ) = ; 4 0