Metamath Proof Explorer


Theorem 2p4e6

Description: 2 + 4 = 6. (Contributed by SN, 24-Aug-2026)

Ref Expression
Assertion 2p4e6
|- ( 2 + 4 ) = 6

Proof

Step Hyp Ref Expression
1 2cn
 |-  2 e. CC
2 1 1 1 addassi
 |-  ( ( 2 + 2 ) + 2 ) = ( 2 + ( 2 + 2 ) )
3 2p2e4
 |-  ( 2 + 2 ) = 4
4 3 oveq1i
 |-  ( ( 2 + 2 ) + 2 ) = ( 4 + 2 )
5 4p2e6
 |-  ( 4 + 2 ) = 6
6 4 5 eqtri
 |-  ( ( 2 + 2 ) + 2 ) = 6
7 3 oveq2i
 |-  ( 2 + ( 2 + 2 ) ) = ( 2 + 4 )
8 2 6 7 3eqtr3ri
 |-  ( 2 + 4 ) = 6