Theorem feq2d

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

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

Proof

Step	Hyp	Ref	Expression
1		feq2d.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
2		feq2	⊢ ( 𝐴 = 𝐵 → ( 𝐹 : 𝐴 ⟶ 𝐶 ↔ 𝐹 : 𝐵 ⟶ 𝐶 ) )
3	1 2	syl	⊢ ( 𝜑 → ( 𝐹 : 𝐴 ⟶ 𝐶 ↔ 𝐹 : 𝐵 ⟶ 𝐶 ) )