Theorem fneq12d

Description: Equality deduction for function predicate with domain. (Contributed by NM, 26-Jun-2011)

	Ref	Expression
Hypotheses	fneq12d.1	$$⊢\phi \to F=G$$
	fneq12d.2	$$⊢\phi \to A=B$$
Assertion	fneq12d	$$⊢\phi \to \left(FFnA\leftrightarrow GFnB\right)$$

Proof

Step	Hyp	Ref	Expression
1		fneq12d.1	$$⊢\phi \to F=G$$
2		fneq12d.2	$$⊢\phi \to A=B$$
3	1	fneq1d	$$⊢\phi \to \left(FFnA\leftrightarrow GFnA\right)$$
4	2	fneq2d	$$⊢\phi \to \left(GFnA\leftrightarrow GFnB\right)$$
5	3 4	bitrd	$$⊢\phi \to \left(FFnA\leftrightarrow GFnB\right)$$