Metamath Proof Explorer


Theorem nfmo

Description: Bound-variable hypothesis builder for the at-most-one quantifier. Note that x and y need not be disjoint. Usage of this theorem is discouraged because it depends on ax-13 . Use the weaker nfmov when possible. (Contributed by NM, 9-Mar-1995) (New usage is discouraged.)

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

Proof

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