Theorem feq3dd

Description: Equality deduction for functions. (Contributed by Thierry Arnoux, 27-May-2025)

	Ref	Expression
Hypotheses	feq3dd.eq	⊢ ( 𝜑 → 𝐵 = 𝐶 )
	feq3dd.f	⊢ ( 𝜑 → 𝐹 : 𝐴 ⟶ 𝐵 )
Assertion	feq3dd	⊢ ( 𝜑 → 𝐹 : 𝐴 ⟶ 𝐶 )

Proof

Step	Hyp	Ref	Expression
1		feq3dd.eq	⊢ ( 𝜑 → 𝐵 = 𝐶 )
2		feq3dd.f	⊢ ( 𝜑 → 𝐹 : 𝐴 ⟶ 𝐵 )
3	1	feq3d	⊢ ( 𝜑 → ( 𝐹 : 𝐴 ⟶ 𝐵 ↔ 𝐹 : 𝐴 ⟶ 𝐶 ) )
4	2 3	mpbid	⊢ ( 𝜑 → 𝐹 : 𝐴 ⟶ 𝐶 )