Metamath Proof Explorer


Theorem nfcrii

Description: Consequence of the not-free predicate. (Contributed by Mario Carneiro, 11-Aug-2016) Avoid ax-10 , ax-11 . (Revised by Gino Giotto, 23-May-2024)

Ref Expression
Hypothesis nfcrii.1
|- F/_ x A
Assertion nfcrii
|- ( y e. A -> A. x y e. A )

Proof

Step Hyp Ref Expression
1 nfcrii.1
 |-  F/_ x A
2 1 nfcri
 |-  F/ x y e. A
3 2 nf5ri
 |-  ( y e. A -> A. x y e. A )