Metamath Proof Explorer


Theorem unexd

Description: The union of two sets is a set. (Contributed by SN, 16-Jul-2024)

Ref Expression
Hypotheses unexd.1 φ A V
unexd.2 φ B W
Assertion unexd φ A B V

Proof

Step Hyp Ref Expression
1 unexd.1 φ A V
2 unexd.2 φ B W
3 unexg A V B W A B V
4 1 2 3 syl2anc φ A B V