Theorem nfcd 2613

Description: Deduce that a class does not have free in it. (Contributed by Mario Carneiro, 11-Aug-2016.)

Hypotheses

Ref	Expression
nfcd.1
nfcd.2

Assertion

Ref	Expression
nfcd

Distinct variable groups:   ,   ,

Proof of Theorem nfcd

Step	Hyp	Ref	Expression
1		nfcd.1	. . 3
2		nfcd.2	. . 3
3	1, 2	alrimi 1877	. 2
4		df-nfc 2607	. 2
5	3, 4	sylibr 212	1

Syntax hints:  ->wi 4  A.wal 1393  F/wnf 1616  e.wcel 1818  F/_wnfc 2605

This theorem is referenced by:  nfabd2  2640  dvelimdc  2642  sbnfc2  3854

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-12 1854

This theorem depends on definitions:  df-bi 185  df-ex 1613  df-nf 1617  df-nfc 2607