Theorem bnj918

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

	Ref	Expression
Hypothesis	bnj918.1	$$⊢G=f\cup \left\{⟨n,C⟩\right\}$$
Assertion	bnj918	$$⊢G\in \mathrm{V}$$

Proof

Step	Hyp	Ref	Expression
1		bnj918.1	$$⊢G=f\cup \left\{⟨n,C⟩\right\}$$
2		vex	$$⊢f\in \mathrm{V}$$
3		snex	$$⊢\left\{⟨n,C⟩\right\}\in \mathrm{V}$$
4	2 3	unex	$$⊢f\cup \left\{⟨n,C⟩\right\}\in \mathrm{V}$$
5	1 4	eqeltri	$$⊢G\in \mathrm{V}$$