Theorem rev0

Description: The empty word is its own reverse. (Contributed by Stefan O'Rear, 26-Aug-2015)

	Ref	Expression
Assertion	rev0	|- ( reverse ` (/) ) = (/)

Proof

Step	Hyp	Ref	Expression
1		wrd0	|- (/) e. Word _V
2		revlen	|- ( (/) e. Word _V -> ( # ` ( reverse ` (/) ) ) = ( # ` (/) ) )
3	1 2	ax-mp	|- ( # ` ( reverse ` (/) ) ) = ( # ` (/) )
4		hash0	|- ( # ` (/) ) = 0
5	3 4	eqtri	|- ( # ` ( reverse ` (/) ) ) = 0
6		fvex	|- ( reverse ` (/) ) e. _V
7		hasheq0	|- ( ( reverse ` (/) ) e. _V -> ( ( # ` ( reverse ` (/) ) ) = 0 <-> ( reverse ` (/) ) = (/) ) )
8	6 7	ax-mp	|- ( ( # ` ( reverse ` (/) ) ) = 0 <-> ( reverse ` (/) ) = (/) )
9	5 8	mpbi	|- ( reverse ` (/) ) = (/)