Metamath Proof Explorer


Theorem nfsbd

Description: Deduction version of nfsb . (Contributed by NM, 15-Feb-2013) Usage of this theorem is discouraged because it depends on ax-13 . Use nfsbv instead. (New usage is discouraged.)

Ref Expression
Hypotheses nfsbd.1 xφ
nfsbd.2 φzψ
Assertion nfsbd φzyxψ

Proof

Step Hyp Ref Expression
1 nfsbd.1 xφ
2 nfsbd.2 φzψ
3 1 2 alrimi φxzψ
4 nfsb4t xzψ¬zz=yzyxψ
5 3 4 syl φ¬zz=yzyxψ
6 axc16nf zz=yzyxψ
7 5 6 pm2.61d2 φzyxψ