Theorem feq1i

Description: Equality inference for functions. (Contributed by Paul Chapman, 22-Jun-2011)

	Ref	Expression
Hypothesis	feq1i.1	⊢ 𝐹 = 𝐺
Assertion	feq1i	⊢ ( 𝐹 : 𝐴 ⟶ 𝐵 ↔ 𝐺 : 𝐴 ⟶ 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		feq1i.1	⊢ 𝐹 = 𝐺
2		feq1	⊢ ( 𝐹 = 𝐺 → ( 𝐹 : 𝐴 ⟶ 𝐵 ↔ 𝐺 : 𝐴 ⟶ 𝐵 ) )
3	1 2	ax-mp	⊢ ( 𝐹 : 𝐴 ⟶ 𝐵 ↔ 𝐺 : 𝐴 ⟶ 𝐵 )