Theorem fssd

Description: Expanding the codomain of a mapping, deduction form. (Contributed by Glauco Siliprandi, 11-Dec-2019)

	Ref	Expression
Hypotheses	fssd.f	|- ( ph -> F : A --> B )
	fssd.b	|- ( ph -> B C_ C )
Assertion	fssd	|- ( ph -> F : A --> C )

Proof

Step	Hyp	Ref	Expression
1		fssd.f	|- ( ph -> F : A --> B )
2		fssd.b	|- ( ph -> B C_ C )
3		fss	|- ( ( F : A --> B /\ B C_ C ) -> F : A --> C )
4	1 2 3	syl2anc	|- ( ph -> F : A --> C )