Metamath Proof Explorer


Theorem 3p5e8

Description: 3 + 5 = 8. (Contributed by SN, 24-Aug-2026)

Ref Expression
Assertion 3p5e8
|- ( 3 + 5 ) = 8

Proof

Step Hyp Ref Expression
1 3cn
 |-  3 e. CC
2 2cn
 |-  2 e. CC
3 1 2 1 addassi
 |-  ( ( 3 + 2 ) + 3 ) = ( 3 + ( 2 + 3 ) )
4 3p2e5
 |-  ( 3 + 2 ) = 5
5 4 oveq1i
 |-  ( ( 3 + 2 ) + 3 ) = ( 5 + 3 )
6 5p3e8
 |-  ( 5 + 3 ) = 8
7 5 6 eqtri
 |-  ( ( 3 + 2 ) + 3 ) = 8
8 2p3e5
 |-  ( 2 + 3 ) = 5
9 8 oveq2i
 |-  ( 3 + ( 2 + 3 ) ) = ( 3 + 5 )
10 3 7 9 3eqtr3ri
 |-  ( 3 + 5 ) = 8