Theorem fssd

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

	Ref	Expression
Hypotheses	fssd.f	⊢ ( 𝜑 → 𝐹 : 𝐴 ⟶ 𝐵 )
	fssd.b	⊢ ( 𝜑 → 𝐵 ⊆ 𝐶 )
Assertion	fssd	⊢ ( 𝜑 → 𝐹 : 𝐴 ⟶ 𝐶 )

Proof

Step	Hyp	Ref	Expression
1		fssd.f	⊢ ( 𝜑 → 𝐹 : 𝐴 ⟶ 𝐵 )
2		fssd.b	⊢ ( 𝜑 → 𝐵 ⊆ 𝐶 )
3		fss	⊢ ( ( 𝐹 : 𝐴 ⟶ 𝐵 ∧ 𝐵 ⊆ 𝐶 ) → 𝐹 : 𝐴 ⟶ 𝐶 )
4	1 2 3	syl2anc	⊢ ( 𝜑 → 𝐹 : 𝐴 ⟶ 𝐶 )