Theorem foeq3

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

	Ref	Expression
Assertion	foeq3	|- ( A = B -> ( F : C -onto-> A <-> F : C -onto-> B ) )

Proof

Step	Hyp	Ref	Expression
1		eqeq2	|- ( A = B -> ( ran F = A <-> ran F = B ) )
2	1	anbi2d	|- ( A = B -> ( ( F Fn C /\ ran F = A ) <-> ( F Fn C /\ ran F = B ) ) )
3		df-fo	|- ( F : C -onto-> A <-> ( F Fn C /\ ran F = A ) )
4		df-fo	|- ( F : C -onto-> B <-> ( F Fn C /\ ran F = B ) )
5	2 3 4	3bitr4g	|- ( A = B -> ( F : C -onto-> A <-> F : C -onto-> B ) )