Metamath Proof Explorer

Theorem 5t5e25

Description: 5 times 5 equals 25. (Contributed by Mario Carneiro, 19-Apr-2015) (Revised by AV, 6-Sep-2021)

Ref Expression
Assertion 5t5e25 
|- ( 5 x. 5 ) = ; 2 5

Proof

Step Hyp Ref Expression
1 5nn0 
 |-  5 e. NN0
2 4nn0 
 |-  4 e. NN0
3 df-5 
 |-  5 = ( 4 + 1 )
4 5t4e20 
 |-  ( 5 x. 4 ) = ; 2 0
5 2nn0 
 |-  2 e. NN0
6 5 dec0u 
 |-  ( ; 1 0 x. 2 ) = ; 2 0
7 4 6 eqtr4i 
 |-  ( 5 x. 4 ) = ( ; 1 0 x. 2 )
8 dfdec10 
 |-  ; 2 5 = ( ( ; 1 0 x. 2 ) + 5 )
9 8 eqcomi 
 |-  ( ( ; 1 0 x. 2 ) + 5 ) = ; 2 5
10 1 2 3 7 9 4t3lem 
 |-  ( 5 x. 5 ) = ; 2 5