Theorem ex-eprel

Description: Example for df-eprel . Example by David A. Wheeler. (Contributed by Mario Carneiro, 18-Jun-2015)

	Ref	Expression
Assertion	ex-eprel	$$⊢5\mathrm{E}\left\{1,5\right\}$$

Proof

Step	Hyp	Ref	Expression
1		5nn	$$⊢5\in \mathbb{N}$$
2	1	elexi	$$⊢5\in \mathrm{V}$$
3	2	prid2	$$⊢5\in \left\{1,5\right\}$$
4		prex	$$⊢\left\{1,5\right\}\in \mathrm{V}$$
5	4	epeli	$$⊢5\mathrm{E}\left\{1,5\right\}\leftrightarrow 5\in \left\{1,5\right\}$$
6	3 5	mpbir	$$⊢5\mathrm{E}\left\{1,5\right\}$$