Theorem feq2i

Description: Equality inference for functions. (Contributed by NM, 5-Sep-2011)

	Ref	Expression
Hypothesis	feq2i.1	⊢ 𝐴 = 𝐵
Assertion	feq2i	⊢ ( 𝐹 : 𝐴 ⟶ 𝐶 ↔ 𝐹 : 𝐵 ⟶ 𝐶 )

Proof

Step	Hyp	Ref	Expression
1		feq2i.1	⊢ 𝐴 = 𝐵
2		feq2	⊢ ( 𝐴 = 𝐵 → ( 𝐹 : 𝐴 ⟶ 𝐶 ↔ 𝐹 : 𝐵 ⟶ 𝐶 ) )
3	1 2	ax-mp	⊢ ( 𝐹 : 𝐴 ⟶ 𝐶 ↔ 𝐹 : 𝐵 ⟶ 𝐶 )