Theorem nfmpt1

Description: Bound-variable hypothesis builder for the maps-to notation. (Contributed by FL, 17-Feb-2008)

	Ref	Expression
Assertion	nfmpt1	⊢ Ⅎ 𝑥 ( 𝑥 ∈ 𝐴 ↦ 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		df-mpt	⊢ ( 𝑥 ∈ 𝐴 ↦ 𝐵 ) = { ⟨ 𝑥 , 𝑧 ⟩ ∣ ( 𝑥 ∈ 𝐴 ∧ 𝑧 = 𝐵 ) }
2		nfopab1	⊢ Ⅎ 𝑥 { ⟨ 𝑥 , 𝑧 ⟩ ∣ ( 𝑥 ∈ 𝐴 ∧ 𝑧 = 𝐵 ) }
3	1 2	nfcxfr	⊢ Ⅎ 𝑥 ( 𝑥 ∈ 𝐴 ↦ 𝐵 )