I am your father

Statement 1 : If Darth Vader is Padme's husband, then Padme has a son with Darth Vader, and if Padme has a son with Darth Vader, then Darth Vader is Luke's father.

Statement 2 : If Darth Vader is not Luke's father, then Padme doesn't have a son with Darth Vader, and if Padme doesn't have a son with Darth Vader, then Darth Vader is not Padme's husband.

If statement 1 is true, is statement 2 true as well?

Credit: Lucasfilm.