Metamath Proof Explorer


Theorem nfmod

Description: Bound-variable hypothesis builder for the at-most-one quantifier. Deduction version of nfmo . Usage of this theorem is discouraged because it depends on ax-13 . Use the weaker nfmodv when possible. (Contributed by Mario Carneiro, 14-Nov-2016) (New usage is discouraged.)

Ref Expression
Hypotheses nfmod.1 yφ
nfmod.2 φxψ
Assertion nfmod φx*yψ

Proof

Step Hyp Ref Expression
1 nfmod.1 yφ
2 nfmod.2 φxψ
3 2 adantr φ¬xx=yxψ
4 1 3 nfmod2 φx*yψ