Theorem nfopab

Description: Bound-variable hypothesis builder for class abstraction. (Contributed by NM, 1-Sep-1999) Remove disjoint variable conditions. (Revised by Andrew Salmon, 11-Jul-2011) (Revised by Scott Fenton, 26-Oct-2024)

	Ref	Expression
Hypothesis	nfopab.1	|- F/ z ph
Assertion	nfopab	|- F/_ z { <. x , y >. | ph }

Proof

Step	Hyp	Ref	Expression
1		nfopab.1	|- F/ z ph
2		nftru	|- F/ x T.
3		nftru	|- F/ y T.
4	1	a1i	|- ( T. -> F/ z ph )
5	2 3 4	nfopabd	|- ( T. -> F/_ z { <. x , y >. | ph } )
6	5	mptru	|- F/_ z { <. x , y >. | ph }