Metamath Proof Explorer


Theorem 2p6e8

Description: 2 + 6 = 8. (Contributed by SN, 24-Aug-2026)

Ref Expression
Assertion 2p6e8
|- ( 2 + 6 ) = 8

Proof

Step Hyp Ref Expression
1 2cn
 |-  2 e. CC
2 4cn
 |-  4 e. CC
3 1 1 2 addassi
 |-  ( ( 2 + 2 ) + 4 ) = ( 2 + ( 2 + 4 ) )
4 2p2e4
 |-  ( 2 + 2 ) = 4
5 4 oveq1i
 |-  ( ( 2 + 2 ) + 4 ) = ( 4 + 4 )
6 4p4e8
 |-  ( 4 + 4 ) = 8
7 5 6 eqtri
 |-  ( ( 2 + 2 ) + 4 ) = 8
8 2p4e6
 |-  ( 2 + 4 ) = 6
9 8 oveq2i
 |-  ( 2 + ( 2 + 4 ) ) = ( 2 + 6 )
10 3 7 9 3eqtr3ri
 |-  ( 2 + 6 ) = 8