Theorem feq3d

Description: Equality deduction for functions. (Contributed by AV, 1-Jan-2020)

	Ref	Expression
Hypothesis	feq2d.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
Assertion	feq3d	⊢ ( 𝜑 → ( 𝐹 : 𝑋 ⟶ 𝐴 ↔ 𝐹 : 𝑋 ⟶ 𝐵 ) )

Proof

Step	Hyp	Ref	Expression
1		feq2d.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
2		feq3	⊢ ( 𝐴 = 𝐵 → ( 𝐹 : 𝑋 ⟶ 𝐴 ↔ 𝐹 : 𝑋 ⟶ 𝐵 ) )
3	1 2	syl	⊢ ( 𝜑 → ( 𝐹 : 𝑋 ⟶ 𝐴 ↔ 𝐹 : 𝑋 ⟶ 𝐵 ) )