Theorem 7p3e10

Description: 7 + 3 = 10. (Contributed by NM, 5-Feb-2007) (Revised by Stanislas Polu, 7-Apr-2020) (Revised by AV, 6-Sep-2021)

	Ref	Expression
Assertion	7p3e10	⊢ ( 7 + 3 ) = ; 1 0

Proof

Step	Hyp	Ref	Expression
1		df-3	⊢ 3 = ( 2 + 1 )
2	1	oveq2i	⊢ ( 7 + 3 ) = ( 7 + ( 2 + 1 ) )
3		7cn	⊢ 7 ∈ ℂ
4		2cn	⊢ 2 ∈ ℂ
5		ax-1cn	⊢ 1 ∈ ℂ
6	3 4 5	addassi	⊢ ( ( 7 + 2 ) + 1 ) = ( 7 + ( 2 + 1 ) )
7	2 6	eqtr4i	⊢ ( 7 + 3 ) = ( ( 7 + 2 ) + 1 )
8		7p2e9	⊢ ( 7 + 2 ) = 9
9	8	oveq1i	⊢ ( ( 7 + 2 ) + 1 ) = ( 9 + 1 )
10		9p1e10	⊢ ( 9 + 1 ) = ; 1 0
11	7 9 10	3eqtri	⊢ ( 7 + 3 ) = ; 1 0