Metamath Proof Explorer


Theorem nfoprab1

Description: The abstraction variables in an operation class abstraction are not free. (Contributed by NM, 25-Apr-1995) (Revised by David Abernethy, 19-Jun-2012)

Ref Expression
Assertion nfoprab1
|- F/_ x { <. <. x , y >. , z >. | ph }

Proof

Step Hyp Ref Expression
1 df-oprab
 |-  { <. <. x , y >. , z >. | ph } = { w | E. x E. y E. z ( w = <. <. x , y >. , z >. /\ ph ) }
2 nfe1
 |-  F/ x E. x E. y E. z ( w = <. <. x , y >. , z >. /\ ph )
3 2 nfab
 |-  F/_ x { w | E. x E. y E. z ( w = <. <. x , y >. , z >. /\ ph ) }
4 1 3 nfcxfr
 |-  F/_ x { <. <. x , y >. , z >. | ph }