Theorem funeqi

Description: Equality inference for the function predicate. (Contributed by Jonathan Ben-Naim, 3-Jun-2011)

	Ref	Expression
Hypothesis	funeqi.1	⊢ 𝐴 = 𝐵
Assertion	funeqi	⊢ ( Fun 𝐴 ↔ Fun 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		funeqi.1	⊢ 𝐴 = 𝐵
2		funeq	⊢ ( 𝐴 = 𝐵 → ( Fun 𝐴 ↔ Fun 𝐵 ) )
3	1 2	ax-mp	⊢ ( Fun 𝐴 ↔ Fun 𝐵 )