Theorem feq1d

Description: Equality deduction for functions. (Contributed by NM, 19-Feb-2008)

	Ref	Expression
Hypothesis	feq1d.1	$$⊢\phi \to F=G$$
Assertion	feq1d	$$⊢\phi \to \left(F:A⟶B\leftrightarrow G:A⟶B\right)$$

Proof

Step	Hyp	Ref	Expression
1		feq1d.1	$$⊢\phi \to F=G$$
2		feq1	$$⊢F=G\to \left(F:A⟶B\leftrightarrow G:A⟶B\right)$$
3	1 2	syl	$$⊢\phi \to \left(F:A⟶B\leftrightarrow G:A⟶B\right)$$