Theorem foeq2

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

	Ref	Expression
Assertion	foeq2	|- ( A = B -> ( F : A -onto-> C <-> F : B -onto-> C ) )

Proof

Step	Hyp	Ref	Expression
1		fneq2	|- ( A = B -> ( F Fn A <-> F Fn B ) )
2	1	anbi1d	|- ( A = B -> ( ( F Fn A /\ ran F = C ) <-> ( F Fn B /\ ran F = C ) ) )
3		df-fo	|- ( F : A -onto-> C <-> ( F Fn A /\ ran F = C ) )
4		df-fo	|- ( F : B -onto-> C <-> ( F Fn B /\ ran F = C ) )
5	2 3 4	3bitr4g	|- ( A = B -> ( F : A -onto-> C <-> F : B -onto-> C ) )