Theorem bnj519

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (Revised by Mario Carneiro, 6-May-2015) (New usage is discouraged.)

	Ref	Expression
Hypothesis	bnj519.1	$$⊢A\in \mathrm{V}$$
Assertion	bnj519	$$⊢B\in \mathrm{V}\to \mathrm{Fun}\left\{⟨A,B⟩\right\}$$

Proof

Step	Hyp	Ref	Expression
1		bnj519.1	$$⊢A\in \mathrm{V}$$
2		funsng	$$⊢\left(A\in \mathrm{V}\wedge B\in \mathrm{V}\right)\to \mathrm{Fun}\left\{⟨A,B⟩\right\}$$
3	1 2	mpan	$$⊢B\in \mathrm{V}\to \mathrm{Fun}\left\{⟨A,B⟩\right\}$$