Theorem fneq2d

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

	Ref	Expression
Hypothesis	fneq2d.1	$$⊢\phi \to A=B$$
Assertion	fneq2d	$$⊢\phi \to \left(FFnA\leftrightarrow FFnB\right)$$

Proof

Step	Hyp	Ref	Expression
1		fneq2d.1	$$⊢\phi \to A=B$$
2		fneq2	$$⊢A=B\to \left(FFnA\leftrightarrow FFnB\right)$$
3	1 2	syl	$$⊢\phi \to \left(FFnA\leftrightarrow FFnB\right)$$