Metamath Proof Explorer


Theorem 3p6e9

Description: 3 + 6 = 9. (Contributed by SN, 24-Aug-2026)

Ref Expression
Assertion 3p6e9
|- ( 3 + 6 ) = 9

Proof

Step Hyp Ref Expression
1 3cn
 |-  3 e. CC
2 1 1 1 addassi
 |-  ( ( 3 + 3 ) + 3 ) = ( 3 + ( 3 + 3 ) )
3 3p3e6
 |-  ( 3 + 3 ) = 6
4 3 oveq1i
 |-  ( ( 3 + 3 ) + 3 ) = ( 6 + 3 )
5 6p3e9
 |-  ( 6 + 3 ) = 9
6 4 5 eqtri
 |-  ( ( 3 + 3 ) + 3 ) = 9
7 3 oveq2i
 |-  ( 3 + ( 3 + 3 ) ) = ( 3 + 6 )
8 2 6 7 3eqtr3ri
 |-  ( 3 + 6 ) = 9