Theorem bj-pr0moore

Description: A pair containing the empty set is a Moore collection. (Contributed by BJ, 4-Oct-2026)

	Ref	Expression
Assertion	bj-pr0moore	$$⊢\left\{\varnothing ,A\right\}\in \underset{\_}{\mathrm{Moore}}$$

Proof

Step	Hyp	Ref	Expression
1		0ex	$$⊢\varnothing \in \mathrm{V}$$
2		0ss	$$⊢\varnothing \subseteq A$$
3		bj-prmoore	$$⊢\left(\varnothing \in \mathrm{V}\wedge \varnothing \subseteq A\right)\to \left\{\varnothing ,A\right\}\in \underset{\_}{\mathrm{Moore}}$$
4	1 2 3	mp2an	$$⊢\left\{\varnothing ,A\right\}\in \underset{\_}{\mathrm{Moore}}$$