Theorem nfr 1411

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

Assertion

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

Proof of Theorem nfr

Step	Hyp	Ref	Expression
1		df-nf 1350	. 2 |- ( F/ x ph <-> A. x ( ph -> A. x ph ) )
2		sp 1401	. 2 |- ( A. x ( ph -> A. x ph ) -> ( ph -> A. x ph ) )
3	1, 2	sylbi 114	1 |- ( F/ x ph -> ( ph -> A. x ph ) )

Syntax hints:   -> wi 4   A.wal 1241   F/wnf 1349

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-4 1400

This theorem depends on definitions:  df-bi 110  df-nf 1350

This theorem is referenced by:  nfri  1412  nfrd  1413  nfimd  1477  19.23t  1567  equs5or  1711  sbequi  1720  sbft  1728  sbcomxyyz  1846  rgen2a  2375