Theorem feq1dd

Description: Equality deduction for functions. (Contributed by Glauco Siliprandi, 11-Dec-2019)

	Ref	Expression
Hypotheses	feq1dd.eq	⊢ ( 𝜑 → 𝐹 = 𝐺 )
	feq1dd.f	⊢ ( 𝜑 → 𝐹 : 𝐴 ⟶ 𝐵 )
Assertion	feq1dd	⊢ ( 𝜑 → 𝐺 : 𝐴 ⟶ 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		feq1dd.eq	⊢ ( 𝜑 → 𝐹 = 𝐺 )
2		feq1dd.f	⊢ ( 𝜑 → 𝐹 : 𝐴 ⟶ 𝐵 )
3	1	feq1d	⊢ ( 𝜑 → ( 𝐹 : 𝐴 ⟶ 𝐵 ↔ 𝐺 : 𝐴 ⟶ 𝐵 ) )
4	2 3	mpbid	⊢ ( 𝜑 → 𝐺 : 𝐴 ⟶ 𝐵 )