Theorem nfr 1408

Description: Consequence of the definition of not-free. (Contributed by Mario Carneiro, 26-Sep-2016.)

Assertion

Ref	Expression
nfr	|- ( F/xph -> (ph -> A.xph))

Proof of Theorem nfr

Step	Hyp	Ref	Expression
1		df-nf 1347	. 2 |- ( F/xph <-> A.x(ph -> A.xph))
2		sp 1398	. 2 |- (A.x(ph -> A.xph) -> (ph -> A.xph))
3	1, 2	sylbi 114	1 |- ( F/xph -> (ph -> A.xph))

Syntax hints:   -> wi 4  A.wal 1240   F/wnf 1346

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-4 1397

This theorem depends on definitions:  df-bi 110  df-nf 1347

This theorem is referenced by:  nfri  1409  nfrd  1410  nfimd  1474  19.23t  1564  equs5or  1708  sbequi  1717  sbft  1725  sbcomxyyz  1843  rgen2a  2369