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 ∈ V
Assertion	bnj519	⊢ ( 𝐵 ∈ V → Fun { ⟨ 𝐴 , 𝐵 ⟩ } )

Proof

Step	Hyp	Ref	Expression
1		bnj519.1	⊢ 𝐴 ∈ V
2		funsng	⊢ ( ( 𝐴 ∈ V ∧ 𝐵 ∈ V ) → Fun { ⟨ 𝐴 , 𝐵 ⟩ } )
3	1 2	mpan	⊢ ( 𝐵 ∈ V → Fun { ⟨ 𝐴 , 𝐵 ⟩ } )