Metamath Proof Explorer

Theorem 8t4e32

Description: 8 times 4 equals 32. (Contributed by Mario Carneiro, 19-Apr-2015)

Ref Expression
Assertion 8t4e32 
|- ( 8 x. 4 ) = ; 3 2

Proof

Step Hyp Ref Expression
1 8nn0 
 |-  8 e. NN0
2 3nn0 
 |-  3 e. NN0
3 df-4 
 |-  4 = ( 3 + 1 )
4 8t3e24 
 |-  ( 8 x. 3 ) = ; 2 4
5 2nn0 
 |-  2 e. NN0
6 4nn0 
 |-  4 e. NN0
7 eqid 
 |-  ; 2 4 = ; 2 4
8 2p1e3 
 |-  ( 2 + 1 ) = 3
9 1 nn0cni 
 |-  8 e. CC
10 6 nn0cni 
 |-  4 e. CC
11 8p4e12 
 |-  ( 8 + 4 ) = ; 1 2
12 9 10 11 addcomli 
 |-  ( 4 + 8 ) = ; 1 2
13 5 6 1 7 8 5 12 decaddci 
 |-  ( ; 2 4 + 8 ) = ; 3 2
14 1 2 3 4 13 4t3lem 
 |-  ( 8 x. 4 ) = ; 3 2