Theorem nfcrii 2611

Description: Consequence of the not-free predicate. (Contributed by Mario Carneiro, 11-Aug-2016.)

Hypothesis

Ref	Expression
nfcri.1

Assertion

Ref	Expression
nfcrii

Distinct variable group:   ,

Proof of Theorem nfcrii

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		nfcri.1	. . . 4
2		nfcr 2610	. . . 4
3	1, 2	ax-mp 5	. . 3
4	3	nfri 1874	. 2
5	4	hblem 2580	1

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

This theorem is referenced by:  nfcri  2612  cleqf  2646  abeq2f  27398  bnj1230  33861  bnj1000  33999  bnj1204  34068  bnj1307  34079  bnj1311  34080  bnj1398  34090  bnj1466  34109  bnj1467  34110  bnj1523  34127

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-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-ex 1613  df-nf 1617  df-sb 1740  df-cleq 2449  df-clel 2452  df-nfc 2607