Metamath Proof Explorer


Theorem nfralw

Description: Bound-variable hypothesis builder for restricted quantification. Version of nfral with a disjoint variable condition, which does not require ax-13 . (Contributed by NM, 1-Sep-1999) (Revised by Gino Giotto, 10-Jan-2024)

Ref Expression
Hypotheses nfralw.1 _xA
nfralw.2 xφ
Assertion nfralw xyAφ

Proof

Step Hyp Ref Expression
1 nfralw.1 _xA
2 nfralw.2 xφ
3 nftru y
4 1 a1i _xA
5 2 a1i xφ
6 3 4 5 nfraldw xyAφ
7 6 mptru xyAφ