Theorem bnj1422

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

	Ref	Expression
Hypotheses	bnj1422.1	$$⊢\phi \to \mathrm{Fun}A$$
	bnj1422.2	$$⊢\phi \to \mathrm{dom}A=B$$
Assertion	bnj1422	$$⊢\phi \to AFnB$$

Proof

Step	Hyp	Ref	Expression
1		bnj1422.1	$$⊢\phi \to \mathrm{Fun}A$$
2		bnj1422.2	$$⊢\phi \to \mathrm{dom}A=B$$
3		df-fn	$$⊢AFnB\leftrightarrow \left(\mathrm{Fun}A\wedge \mathrm{dom}A=B\right)$$
4	1 2 3	sylanbrc	$$⊢\phi \to AFnB$$