Theorem ifhvhv0

Description: Prove if ( A e. ~H , A , 0h ) e. ~H . (Contributed by David A. Wheeler, 7-Dec-2018) (New usage is discouraged.)

	Ref	Expression
Assertion	ifhvhv0	⊢ if ( 𝐴 ∈ ℋ , 𝐴 , 0ℎ ) ∈ ℋ

Proof

Step	Hyp	Ref	Expression
1		ax-hv0cl	⊢ 0ℎ ∈ ℋ
2	1	elimel	⊢ if ( 𝐴 ∈ ℋ , 𝐴 , 0ℎ ) ∈ ℋ