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Metamath Proof Explorer

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	$⊢ F = \{⟨2, 6⟩, ⟨3, 9⟩\} \to F (3) = 9$

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