Metamath Proof Explorer


Theorem unnum

Description: The union of two numerable sets is numerable. (Contributed by Mario Carneiro, 29-Apr-2015)

Ref Expression
Assertion unnum AdomcardBdomcardABdomcard

Proof

Step Hyp Ref Expression
1 djunum AdomcardBdomcardA⊔︀Bdomcard
2 undjudom AdomcardBdomcardABA⊔︀B
3 numdom A⊔︀BdomcardABA⊔︀BABdomcard
4 1 2 3 syl2anc AdomcardBdomcardABdomcard