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Metamath Proof Explorer

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	$⊢ if (A \in ℋ, A, 0_{ℎ}) \in ℋ$

Step	Hyp	Ref	Expression
1		ax-hv0cl	$⊢ 0_{ℎ} \in ℋ$
2	1	elimel	$⊢ if (A \in ℋ, A, 0_{ℎ}) \in ℋ$