Washington (CNN) The House will vote Wednesday on a bill that would let gun owners with permits to carry concealed weapons travel to other states with their concealed firearms.

The bill is a top priority of the National Rifle Association, and since leaving committee it has been combined with an additional measure that is designed to update the federal background check system after holes were exposed by November's mass shooting at a church in Texas.

The move to merge the two pieces of legislation makes it a difficult vote for Democrats.

Second Amendment advocates maintain that gun owners should not lose their right to bear arms as they travel across state lines, and current laws that vary in different states could mean that licensed owners might unintentionally violate the law. Under the proposed law, gun owners would be required to abide by the local and state regulations in place for concealed weapons.

The part of the legislation that aims to update background checks through the National Instant Criminal Background Check System, or NICS, held bipartisan support when it was being considered by the House Judiciary Committee, after more than 20 people were killed at the church in Sutherland Springs, Texas.

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