Metamath Proof Explorer


Theorem nfcrALT

Description: Alternate version of nfcr . Avoids ax-8 but uses ax-12 . (Contributed by Mario Carneiro, 11-Aug-2016) (New usage is discouraged.) (Proof modification is discouraged.)

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

Proof

Step Hyp Ref Expression
1 df-nfc
 |-  ( F/_ x A <-> A. y F/ x y e. A )
2 sp
 |-  ( A. y F/ x y e. A -> F/ x y e. A )
3 1 2 sylbi
 |-  ( F/_ x A -> F/ x y e. A )