Metamath Proof Explorer


Theorem 8t6e48

Description: 8 times 6 equals 48. (Contributed by Mario Carneiro, 19-Apr-2015) (Revised by AV, 6-Sep-2021)

Ref Expression
Assertion 8t6e48
|- ( 8 x. 6 ) = ; 4 8

Proof

Step Hyp Ref Expression
1 8nn0
 |-  8 e. NN0
2 5nn0
 |-  5 e. NN0
3 df-6
 |-  6 = ( 5 + 1 )
4 8t5e40
 |-  ( 8 x. 5 ) = ; 4 0
5 4nn0
 |-  4 e. NN0
6 5 dec0u
 |-  ( ; 1 0 x. 4 ) = ; 4 0
7 4 6 eqtr4i
 |-  ( 8 x. 5 ) = ( ; 1 0 x. 4 )
8 dfdec10
 |-  ; 4 8 = ( ( ; 1 0 x. 4 ) + 8 )
9 8 eqcomi
 |-  ( ( ; 1 0 x. 4 ) + 8 ) = ; 4 8
10 1 2 3 7 9 4t3lem
 |-  ( 8 x. 6 ) = ; 4 8