This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

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 e. ~H , A , 0h ) e. ~H

Proof

Step Hyp Ref Expression
1 ax-hv0cl 
 |-  0h e. ~H
2 1 elimel 
 |-  if ( A e. ~H , A , 0h ) e. ~H