Theorem 5p5e10

Description: 5 + 5 = 10. (Contributed by NM, 5-Feb-2007) (Revised by Stanislas Polu, 7-Apr-2020) (Revised by AV, 6-Sep-2021)

	Ref	Expression
Assertion	5p5e10	⊢ ( 5 + 5 ) = ; 1 0

Proof

Step	Hyp	Ref	Expression
1		df-5	⊢ 5 = ( 4 + 1 )
2	1	oveq2i	⊢ ( 5 + 5 ) = ( 5 + ( 4 + 1 ) )
3		5cn	⊢ 5 ∈ ℂ
4		4cn	⊢ 4 ∈ ℂ
5		ax-1cn	⊢ 1 ∈ ℂ
6	3 4 5	addassi	⊢ ( ( 5 + 4 ) + 1 ) = ( 5 + ( 4 + 1 ) )
7	2 6	eqtr4i	⊢ ( 5 + 5 ) = ( ( 5 + 4 ) + 1 )
8		5p4e9	⊢ ( 5 + 4 ) = 9
9	8	oveq1i	⊢ ( ( 5 + 4 ) + 1 ) = ( 9 + 1 )
10		9p1e10	⊢ ( 9 + 1 ) = ; 1 0
11	7 9 10	3eqtri	⊢ ( 5 + 5 ) = ; 1 0