Theorem ex-fv

Description: Example for df-fv . Example by David A. Wheeler. (Contributed by Mario Carneiro, 7-May-2015)

	Ref	Expression
Assertion	ex-fv	$$⊢F=\left\{⟨2,6⟩,⟨3,9⟩\right\}\to F\left(3\right)=9$$

Proof

Step	Hyp	Ref	Expression
1		fveq1	$$⊢F=\left\{⟨2,6⟩,⟨3,9⟩\right\}\to F\left(3\right)=\left\{⟨2,6⟩,⟨3,9⟩\right\}\left(3\right)$$
2		2re	$$⊢2\in ℝ$$
3		2lt3	$$⊢2<3$$
4	2 3	ltneii	$$⊢2\ne 3$$
5		3ex	$$⊢3\in \mathrm{V}$$
6		9re	$$⊢9\in ℝ$$
7	6	elexi	$$⊢9\in \mathrm{V}$$
8	5 7	fvpr2	$$⊢2\ne 3\to \left\{⟨2,6⟩,⟨3,9⟩\right\}\left(3\right)=9$$
9	4 8	ax-mp	$$⊢\left\{⟨2,6⟩,⟨3,9⟩\right\}\left(3\right)=9$$
10	1 9	syl6eq	$$⊢F=\left\{⟨2,6⟩,⟨3,9⟩\right\}\to F\left(3\right)=9$$