Metamath Proof Explorer

Theorem 8t3e24

Description: 8 times 3 equals 24. (Contributed by Mario Carneiro, 19-Apr-2015)

Ref Expression
Assertion 8t3e24 
|- ( 8 x. 3 ) = ; 2 4

Proof

Step Hyp Ref Expression
1 8nn0 
 |-  8 e. NN0
2 2nn0 
 |-  2 e. NN0
3 df-3 
 |-  3 = ( 2 + 1 )
4 8t2e16 
 |-  ( 8 x. 2 ) = ; 1 6
5 1nn0 
 |-  1 e. NN0
6 6nn0 
 |-  6 e. NN0
7 eqid 
 |-  ; 1 6 = ; 1 6
8 1p1e2 
 |-  ( 1 + 1 ) = 2
9 4nn0 
 |-  4 e. NN0
10 1 nn0cni 
 |-  8 e. CC
11 6 nn0cni 
 |-  6 e. CC
12 8p6e14 
 |-  ( 8 + 6 ) = ; 1 4
13 10 11 12 addcomli 
 |-  ( 6 + 8 ) = ; 1 4
14 5 6 1 7 8 9 13 decaddci 
 |-  ( ; 1 6 + 8 ) = ; 2 4
15 1 2 3 4 14 4t3lem 
 |-  ( 8 x. 3 ) = ; 2 4