Theorem feq2dd

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

	Ref	Expression
Hypotheses	feq2dd.eq	⊢ ( 𝜑 → 𝐴 = 𝐵 )
	feq2dd.f	⊢ ( 𝜑 → 𝐹 : 𝐴 ⟶ 𝐶 )
Assertion	feq2dd	⊢ ( 𝜑 → 𝐹 : 𝐵 ⟶ 𝐶 )

Proof

Step	Hyp	Ref	Expression
1		feq2dd.eq	⊢ ( 𝜑 → 𝐴 = 𝐵 )
2		feq2dd.f	⊢ ( 𝜑 → 𝐹 : 𝐴 ⟶ 𝐶 )
3	1	feq2d	⊢ ( 𝜑 → ( 𝐹 : 𝐴 ⟶ 𝐶 ↔ 𝐹 : 𝐵 ⟶ 𝐶 ) )
4	2 3	mpbid	⊢ ( 𝜑 → 𝐹 : 𝐵 ⟶ 𝐶 )