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 >. } -> ( F ` 3 ) = 9 )

Proof

Step	Hyp	Ref	Expression
1		fveq1	|- ( F = { <. 2 , 6 >. , <. 3 , 9 >. } -> ( F ` 3 ) = ( { <. 2 , 6 >. , <. 3 , 9 >. } ` 3 ) )
2		2re	|- 2 e. RR
3		2lt3	|- 2 < 3
4	2 3	ltneii	|- 2 =/= 3
5		3ex	|- 3 e. _V
6		9re	|- 9 e. RR
7	6	elexi	|- 9 e. _V
8	5 7	fvpr2	|- ( 2 =/= 3 -> ( { <. 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 >. } -> ( F ` 3 ) = 9 )