Theorem feq3

Description: Equality theorem for functions. (Contributed by NM, 1-Aug-1994)

	Ref	Expression
Assertion	feq3	|- ( A = B -> ( F : C --> A <-> F : C --> B ) )

Proof

Step	Hyp	Ref	Expression
1		sseq2	|- ( A = B -> ( ran F C_ A <-> ran F C_ B ) )
2	1	anbi2d	|- ( A = B -> ( ( F Fn C /\ ran F C_ A ) <-> ( F Fn C /\ ran F C_ B ) ) )
3		df-f	|- ( F : C --> A <-> ( F Fn C /\ ran F C_ A ) )
4		df-f	|- ( F : C --> B <-> ( F Fn C /\ ran F C_ B ) )
5	2 3 4	3bitr4g	|- ( A = B -> ( F : C --> A <-> F : C --> B ) )