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	$$⊢if\left(A\in \mathscr{H},A,0_{ℎ}\right)\in \mathscr{H}$$

Proof

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