Metamath Proof Explorer


Theorem 2p3e5

Description: 2 + 3 = 5. (Contributed by SN, 24-Aug-2026)

Ref Expression
Assertion 2p3e5 ( 2 + 3 ) = 5

Proof

Step Hyp Ref Expression
1 2cn ⊢ 2 ∈ ℂ
2 ax-1cn ⊢ 1 ∈ ℂ
3 1 2 1 addassi ⊢ ( ( 2 + 1 ) + 2 ) = ( 2 + ( 1 + 2 ) )
4 2p1e3 ⊢ ( 2 + 1 ) = 3
5 4 oveq1i ⊢ ( ( 2 + 1 ) + 2 ) = ( 3 + 2 )
6 3p2e5 ⊢ ( 3 + 2 ) = 5
7 5 6 eqtri ⊢ ( ( 2 + 1 ) + 2 ) = 5
8 1p2e3 ⊢ ( 1 + 2 ) = 3
9 8 oveq2i ⊢ ( 2 + ( 1 + 2 ) ) = ( 2 + 3 )
10 3 7 9 3eqtr3ri ⊢ ( 2 + 3 ) = 5