Theorem fneq1d

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

	Ref	Expression
Hypothesis	fneq1d.1	$$⊢\phi \to F=G$$
Assertion	fneq1d	$$⊢\phi \to \left(FFnA\leftrightarrow GFnA\right)$$

Proof

Step	Hyp	Ref	Expression
1		fneq1d.1	$$⊢\phi \to F=G$$
2		fneq1	$$⊢F=G\to \left(FFnA\leftrightarrow GFnA\right)$$
3	1 2	syl	$$⊢\phi \to \left(FFnA\leftrightarrow GFnA\right)$$