Axiom ax-hvaddid

Description: Addition with the zero vector. (Contributed by NM, 16-Aug-1999) (New usage is discouraged.)

	Ref	Expression
Assertion	ax-hvaddid	⊢ ( 𝐴 ∈ ℋ → ( 𝐴 +ℎ 0ℎ ) = 𝐴 )

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		cA	⊢ 𝐴
1		chba	⊢ ℋ
2	0 1	wcel	⊢ 𝐴 ∈ ℋ
3		cva	⊢ +ℎ
4		c0v	⊢ 0ℎ
5	0 4 3	co	⊢ ( 𝐴 +ℎ 0ℎ )
6	5 0	wceq	⊢ ( 𝐴 +ℎ 0ℎ ) = 𝐴
7	2 6	wi	⊢ ( 𝐴 ∈ ℋ → ( 𝐴 +ℎ 0ℎ ) = 𝐴 )