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Metamath Proof Explorer

Theorem mptex

Description: If the domain of a function given by maps-to notation is a set, the function is a set. Inference version of mptexg . (Contributed by NM, 22-Apr-2005) (Revised by Mario Carneiro, 20-Dec-2013)

		Ref	Expression
	Hypothesis	mptex.1	⊢ 𝐴 ∈ V
	Assertion	mptex	⊢ ( 𝑥 ∈ 𝐴 ↦ 𝐵 ) ∈ V

Proof

Step	Hyp	Ref	Expression
1		mptex.1	⊢ 𝐴 ∈ V
2		mptexg	⊢ ( 𝐴 ∈ V → ( 𝑥 ∈ 𝐴 ↦ 𝐵 ) ∈ V )
3	1 2	ax-mp	⊢ ( 𝑥 ∈ 𝐴 ↦ 𝐵 ) ∈ V