Theorem funeqi

Description: Equality inference for the function predicate. (Contributed by Jonathan Ben-Naim, 3-Jun-2011)

	Ref	Expression
Hypothesis	funeqi.1	$$⊢A=B$$
Assertion	funeqi	$$⊢\mathrm{Fun}A\leftrightarrow \mathrm{Fun}B$$

Proof

Step	Hyp	Ref	Expression
1		funeqi.1	$$⊢A=B$$
2		funeq	$$⊢A=B\to \left(\mathrm{Fun}A\leftrightarrow \mathrm{Fun}B\right)$$
3	1 2	ax-mp	$$⊢\mathrm{Fun}A\leftrightarrow \mathrm{Fun}B$$