Metamath Proof Explorer


Theorem 5p5e10

Description: 5 + 5 = 10. (Contributed by NM, 5-Feb-2007) (Revised by Stanislas Polu, 7-Apr-2020) (Revised by AV, 6-Sep-2021)

Ref Expression
Assertion 5p5e10
|- ( 5 + 5 ) = ; 1 0

Proof

Step Hyp Ref Expression
1 df-5
 |-  5 = ( 4 + 1 )
2 1 oveq2i
 |-  ( 5 + 5 ) = ( 5 + ( 4 + 1 ) )
3 5cn
 |-  5 e. CC
4 4cn
 |-  4 e. CC
5 ax-1cn
 |-  1 e. CC
6 3 4 5 addassi
 |-  ( ( 5 + 4 ) + 1 ) = ( 5 + ( 4 + 1 ) )
7 2 6 eqtr4i
 |-  ( 5 + 5 ) = ( ( 5 + 4 ) + 1 )
8 5p4e9
 |-  ( 5 + 4 ) = 9
9 8 oveq1i
 |-  ( ( 5 + 4 ) + 1 ) = ( 9 + 1 )
10 9p1e10
 |-  ( 9 + 1 ) = ; 1 0
11 7 9 10 3eqtri
 |-  ( 5 + 5 ) = ; 1 0