Theorem fneq2d

Description: Equality deduction for function predicate with domain. (Contributed by Paul Chapman, 22-Jun-2011)

	Ref	Expression
Hypothesis	fneq2d.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
Assertion	fneq2d	⊢ ( 𝜑 → ( 𝐹 Fn 𝐴 ↔ 𝐹 Fn 𝐵 ) )

Proof

Step	Hyp	Ref	Expression
1		fneq2d.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
2		fneq2	⊢ ( 𝐴 = 𝐵 → ( 𝐹 Fn 𝐴 ↔ 𝐹 Fn 𝐵 ) )
3	1 2	syl	⊢ ( 𝜑 → ( 𝐹 Fn 𝐴 ↔ 𝐹 Fn 𝐵 ) )