Metamath Proof Explorer

Theorem nfrexg

Description: Bound-variable hypothesis builder for restricted quantification. Usage of this theorem is discouraged because it depends on ax-13 . See nfrex for a version with a disjoint variable condition, but not requiring ax-13 . (Contributed by NM, 1-Sep-1999) (Revised by Mario Carneiro, 7-Oct-2016) (Proof shortened by Wolf Lammen, 30-Dec-2019) (New usage is discouraged.)

Ref Expression
Hypotheses nfrexg.1 _ x A
nfrexg.2 x φ
Assertion nfrexg x y A φ


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