Theorem nfnfc1 2767

Description: The setvar x is bound in F/_ x A. (Contributed by Mario Carneiro, 11-Aug-2016.)

Assertion

Ref	Expression
nfnfc1	|- F/ x F/_ x A

Proof of Theorem nfnfc1

Dummy variable y is distinct from all other variables.

Step	Hyp	Ref	Expression
1		df-nfc 2753	. 2 |- ( F/_ x A <-> A. y F/ x y e. A )
2		nfnf1 2031	. . 3 |- F/ x F/ x y e. A
3	2	nfal 2153	. 2 |- F/ x A. y F/ x y e. A
4	1, 3	nfxfr 1779	1 |- F/ x F/_ x A

Syntax hints:   A.wal 1481   F/wnf 1708   e. wcel 1990   F/_wnfc 2751

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-10 2019  ax-11 2034  ax-12 2047

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-ex 1705  df-nf 1710  df-nfc 2753

This theorem is referenced by:  vtoclgft  3254  vtoclgftOLD  3255  sbcralt  3510  sbcrext  3511  sbcrextOLD  3512  csbiebt  3553  nfopd  4419  nfimad  5475  nffvd  6200  nfded  34254  nfded2  34255  nfunidALT2  34256