Theorem f1oeq1d

Description: Equality deduction for one-to-one onto functions. (Contributed by Glauco Siliprandi, 17-Aug-2020)

	Ref	Expression
Hypothesis	f1oeq1d.1	|- ( ph -> F = G )
Assertion	f1oeq1d	|- ( ph -> ( F : A -1-1-onto-> B <-> G : A -1-1-onto-> B ) )

Proof

Step	Hyp	Ref	Expression
1		f1oeq1d.1	|- ( ph -> F = G )
2		f1oeq1	|- ( F = G -> ( F : A -1-1-onto-> B <-> G : A -1-1-onto-> B ) )
3	1 2	syl	|- ( ph -> ( F : A -1-1-onto-> B <-> G : A -1-1-onto-> B ) )