Theorem feq12i

Description: Equality inference for functions. (Contributed by AV, 7-Feb-2021)

	Ref	Expression
Hypotheses	feq12i.1	⊢ 𝐹 = 𝐺
	feq12i.2	⊢ 𝐴 = 𝐵
Assertion	feq12i	⊢ ( 𝐹 : 𝐴 ⟶ 𝐶 ↔ 𝐺 : 𝐵 ⟶ 𝐶 )

Proof

Step	Hyp	Ref	Expression
1		feq12i.1	⊢ 𝐹 = 𝐺
2		feq12i.2	⊢ 𝐴 = 𝐵
3		eqid	⊢ 𝐶 = 𝐶
4		feq123	⊢ ( ( 𝐹 = 𝐺 ∧ 𝐴 = 𝐵 ∧ 𝐶 = 𝐶 ) → ( 𝐹 : 𝐴 ⟶ 𝐶 ↔ 𝐺 : 𝐵 ⟶ 𝐶 ) )
5	1 2 3 4	mp3an	⊢ ( 𝐹 : 𝐴 ⟶ 𝐶 ↔ 𝐺 : 𝐵 ⟶ 𝐶 )