Theorem hbn 1647

Description: If x is not free in ph, it is not free in -. ph. (Contributed by NM, 5-Aug-1993.)

Hypothesis

Ref	Expression
hbn.1	|- ( ph -> A. x ph )

Assertion

Ref	Expression
hbn	|- ( -. ph -> A. x -. ph )

Proof of Theorem hbn

Step	Hyp	Ref	Expression
1		hbnt 1646	. 2 |- ( A. x ( ph -> A. x ph ) -> ( -. ph -> A. x -. ph ) )
2		hbn.1	. 2 |- ( ph -> A. x ph )
3	1, 2	mpg 1444	1 |- ( -. ph -> A. x -. ph )

Syntax hints:   -. wn 3   -> wi 4   A.wal 1346

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 609  ax-in2 610  ax-5 1440  ax-gen 1442  ax-ie2 1487  ax-4 1503  ax-ial 1527

This theorem depends on definitions:  df-bi 116  df-tru 1351  df-fal 1354

This theorem is referenced by:  hbnae  1714  sbn  1945  euor  2045  euor2  2077