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Metamath Proof Explorer

Theorem mptexd

Description: If the domain of a function given by maps-to notation is a set, the function is a set. Deduction version of mptexg . (Contributed by Glauco Siliprandi, 24-Dec-2020)

		Ref	Expression
	Hypothesis	mptexd.1	⊢ ( 𝜑 → 𝐴 ∈ 𝑉 )
	Assertion	mptexd	⊢ ( 𝜑 → ( 𝑥 ∈ 𝐴 ↦ 𝐵 ) ∈ V )

Proof

Step	Hyp	Ref	Expression
1		mptexd.1	⊢ ( 𝜑 → 𝐴 ∈ 𝑉 )
2		mptexg	⊢ ( 𝐴 ∈ 𝑉 → ( 𝑥 ∈ 𝐴 ↦ 𝐵 ) ∈ V )
3	1 2	syl	⊢ ( 𝜑 → ( 𝑥 ∈ 𝐴 ↦ 𝐵 ) ∈ V )