Theorem fneq2i

Description: Equality inference for function predicate with domain. (Contributed by NM, 4-Sep-2011)

	Ref	Expression
Hypothesis	fneq2i.1	⊢ 𝐴 = 𝐵
Assertion	fneq2i	⊢ ( 𝐹 Fn 𝐴 ↔ 𝐹 Fn 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		fneq2i.1	⊢ 𝐴 = 𝐵
2		fneq2	⊢ ( 𝐴 = 𝐵 → ( 𝐹 Fn 𝐴 ↔ 𝐹 Fn 𝐵 ) )
3	1 2	ax-mp	⊢ ( 𝐹 Fn 𝐴 ↔ 𝐹 Fn 𝐵 )