Metamath Proof Explorer


Theorem coexd

Description: The composition of two sets is a set. (Contributed by SN, 7-Feb-2025)

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

Proof

Step Hyp Ref Expression
1 coexd.1 φ A V
2 coexd.2 φ B W
3 coexg A V B W A B V
4 1 2 3 syl2anc φ A B V