Theorem f1oeq2d

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

	Ref	Expression
Hypothesis	f1oeq2d.1	|- ( ph -> A = B )
Assertion	f1oeq2d	|- ( ph -> ( F : A -1-1-onto-> C <-> F : B -1-1-onto-> C ) )

Proof

Step	Hyp	Ref	Expression
1		f1oeq2d.1	|- ( ph -> A = B )
2		f1oeq2	|- ( A = B -> ( F : A -1-1-onto-> C <-> F : B -1-1-onto-> C ) )
3	1 2	syl	|- ( ph -> ( F : A -1-1-onto-> C <-> F : B -1-1-onto-> C ) )