Theorem feq1dd

Description: Equality deduction for functions. (Contributed by Glauco Siliprandi, 11-Dec-2019)

	Ref	Expression
Hypotheses	feq1dd.eq	$$⊢\phi \to F=G$$
	feq1dd.f	$$⊢\phi \to F:A⟶B$$
Assertion	feq1dd	$$⊢\phi \to G:A⟶B$$

Proof

Step	Hyp	Ref	Expression
1		feq1dd.eq	$$⊢\phi \to F=G$$
2		feq1dd.f	$$⊢\phi \to F:A⟶B$$
3	1	feq1d	$$⊢\phi \to \left(F:A⟶B\leftrightarrow G:A⟶B\right)$$
4	2 3	mpbid	$$⊢\phi \to G:A⟶B$$