Theorem feq3d

Description: Equality deduction for functions. (Contributed by AV, 1-Jan-2020)

	Ref	Expression
Hypothesis	feq2d.1	$$⊢\phi \to A=B$$
Assertion	feq3d	$$⊢\phi \to \left(F:X⟶A\leftrightarrow F:X⟶B\right)$$

Proof

Step	Hyp	Ref	Expression
1		feq2d.1	$$⊢\phi \to A=B$$
2		feq3	$$⊢A=B\to \left(F:X⟶A\leftrightarrow F:X⟶B\right)$$
3	1 2	syl	$$⊢\phi \to \left(F:X⟶A\leftrightarrow F:X⟶B\right)$$