Theorem ressunif

Description: UnifSet is unaffected by restriction. (Contributed by Thierry Arnoux, 7-Dec-2017)

	Ref	Expression
Hypotheses	ressunif.1	⊢ 𝐻 = ( 𝐺 ↾s 𝐴 )
	ressunif.2	⊢ 𝑈 = ( UnifSet ‘ 𝐺 )
Assertion	ressunif	⊢ ( 𝐴 ∈ 𝑉 → 𝑈 = ( UnifSet ‘ 𝐻 ) )

Proof

Step	Hyp	Ref	Expression
1		ressunif.1	⊢ 𝐻 = ( 𝐺 ↾s 𝐴 )
2		ressunif.2	⊢ 𝑈 = ( UnifSet ‘ 𝐺 )
3		unifid	⊢ UnifSet = Slot ( UnifSet ‘ ndx )
4		unifndxnbasendx	⊢ ( UnifSet ‘ ndx ) ≠ ( Base ‘ ndx )
5	1 2 3 4	resseqnbas	⊢ ( 𝐴 ∈ 𝑉 → 𝑈 = ( UnifSet ‘ 𝐻 ) )