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 _ x A
nfralw.2 x φ
Assertion nfralw x y A φ


Step Hyp Ref Expression
1 nfralw.1 _ x A
2 nfralw.2 x φ
3 nftru y
4 1 a1i _ x A
5 2 a1i x φ
6 3 4 5 nfraldw x y A φ
7 6 mptru x y A φ