Metamath Proof Explorer

Theorem 6t6e36

Description: 6 times 6 equals 36. (Contributed by Mario Carneiro, 19-Apr-2015) (Revised by AV, 6-Sep-2021)

Ref Expression
Assertion 6t6e36 
|- ( 6 x. 6 ) = ; 3 6

Proof

Step Hyp Ref Expression
1 6nn0 
 |-  6 e. NN0
2 5nn0 
 |-  5 e. NN0
3 df-6 
 |-  6 = ( 5 + 1 )
4 6t5e30 
 |-  ( 6 x. 5 ) = ; 3 0
5 3nn0 
 |-  3 e. NN0
6 5 dec0u 
 |-  ( ; 1 0 x. 3 ) = ; 3 0
7 4 6 eqtr4i 
 |-  ( 6 x. 5 ) = ( ; 1 0 x. 3 )
8 dfdec10 
 |-  ; 3 6 = ( ( ; 1 0 x. 3 ) + 6 )
9 8 eqcomi 
 |-  ( ( ; 1 0 x. 3 ) + 6 ) = ; 3 6
10 1 2 3 7 9 4t3lem 
 |-  ( 6 x. 6 ) = ; 3 6