Theorem nfr 1566

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 1509	. 2 |- ( F/ x ph <-> A. x ( ph -> A. x ph ) )
2		sp 1559	. 2 |- ( A. x ( ph -> A. x ph ) -> ( ph -> A. x ph ) )
3	1, 2	sylbi 121	1 |- ( F/ x ph -> ( ph -> A. x ph ) )

Syntax hints:   -> wi 4   A.wal 1395   F/wnf 1508

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-4 1558

This theorem depends on definitions:  df-bi 117  df-nf 1509

This theorem is referenced by:  nfri  1567  nfrd  1568  nfimd  1633  19.23t  1725  equs5or  1878  sbequi  1887  sbft  1896  sbcomxyyz  2025  rgen2a  2586