Theorem 0exp0e1

Description: 0 ^ 0 = 1 . This is our convention. It follows the convention used by Gleason; see Part of Definition 10-4.1 of Gleason p. 134. (Contributed by David A. Wheeler, 8-Dec-2018)

	Ref	Expression
Assertion	0exp0e1	⊢ ( 0 ↑ 0 ) = 1

Proof

Step	Hyp	Ref	Expression
1		0cn	⊢ 0 ∈ ℂ
2		exp0	⊢ ( 0 ∈ ℂ → ( 0 ↑ 0 ) = 1 )
3	1 2	ax-mp	⊢ ( 0 ↑ 0 ) = 1