Theorem funeqd

Description: Equality deduction for the function predicate. (Contributed by NM, 23-Feb-2013)

	Ref	Expression
Hypothesis	funeqd.1	$$⊢\phi \to A=B$$
Assertion	funeqd	$$⊢\phi \to \left(\mathrm{Fun}A\leftrightarrow \mathrm{Fun}B\right)$$

Proof

Step	Hyp	Ref	Expression
1		funeqd.1	$$⊢\phi \to A=B$$
2		funeq	$$⊢A=B\to \left(\mathrm{Fun}A\leftrightarrow \mathrm{Fun}B\right)$$
3	1 2	syl	$$⊢\phi \to \left(\mathrm{Fun}A\leftrightarrow \mathrm{Fun}B\right)$$