Metamath Proof Explorer


Theorem nfmov

Description: Bound-variable hypothesis builder for the at-most-one quantifier. See nfmo for a version without disjoint variable conditions but requiring ax-13 . (Contributed by NM, 9-Mar-1995) (Revised by Wolf Lammen, 2-Oct-2023)

Ref Expression
Hypothesis nfmov.1
|- F/ x ph
Assertion nfmov
|- F/ x E* y ph

Proof

Step Hyp Ref Expression
1 nfmov.1
 |-  F/ x ph
2 nftru
 |-  F/ y T.
3 1 a1i
 |-  ( T. -> F/ x ph )
4 2 3 nfmodv
 |-  ( T. -> F/ x E* y ph )
5 4 mptru
 |-  F/ x E* y ph