Theorem fneq12

Description: Equality theorem for function predicate with domain. (Contributed by Thierry Arnoux, 31-Jan-2017)

	Ref	Expression
Assertion	fneq12	$$⊢\left(F=G\wedge A=B\right)\to \left(FFnA\leftrightarrow GFnB\right)$$

Proof

Step	Hyp	Ref	Expression
1		simpl	$$⊢\left(F=G\wedge A=B\right)\to F=G$$
2		simpr	$$⊢\left(F=G\wedge A=B\right)\to A=B$$
3	1 2	fneq12d	$$⊢\left(F=G\wedge A=B\right)\to \left(FFnA\leftrightarrow GFnB\right)$$