Theorem nfnfc1 2492

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

Assertion

Ref	Expression
nfnfc1	|- F/x F/_xA

Proof of Theorem nfnfc1

Dummy variable y is distinct from all other variables.

Step	Hyp	Ref	Expression
1		df-nfc 2478	. 2 |- ( F/_xA <-> A.y F/x y e. A)
2		nfnf1 1790	. . 3 |- F/x F/x y e. A
3	2	nfal 1842	. 2 |- F/xA.y F/x y e. A
4	1, 3	nfxfr 1570	1 |- F/x F/_xA

Syntax hints:  A.wal 1540   F/wnf 1544   e. wcel 1710   F/_wnfc 2476

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746

This theorem depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545  df-nfc 2478

This theorem is referenced by:  vtoclgft  2905  sbcralt  3118  sbcrext  3119  csbiebt  3172  nfopd  4605  nfimad  4954  nffvd  5335