Theorem nfr 1498

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 1437	. 2 |- ( F/ x ph <-> A. x ( ph -> A. x ph ) )
2		sp 1488	. 2 |- ( A. x ( ph -> A. x ph ) -> ( ph -> A. x ph ) )
3	1, 2	sylbi 120	1 |- ( F/ x ph -> ( ph -> A. x ph ) )

Syntax hints:   -> wi 4   A.wal 1329   F/wnf 1436

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-4 1487

This theorem depends on definitions:  df-bi 116  df-nf 1437

This theorem is referenced by:  nfri  1499  nfrd  1500  nfimd  1564  19.23t  1655  equs5or  1802  sbequi  1811  sbft  1820  sbcomxyyz  1943  rgen2a  2484