Theorem hbn 1584

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 1583	. 2 |- ( A. x ( ph -> A. x ph ) -> ( -. ph -> A. x -. ph ) )
2		hbn.1	. 2 |- ( ph -> A. x ph )
3	1, 2	mpg 1380	1 |- ( -. ph -> A. x -. ph )

Syntax hints:   -. wn 3   -> wi 4   A.wal 1282

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 576  ax-in2 577  ax-5 1376  ax-gen 1378  ax-ie2 1423  ax-4 1440  ax-ial 1467

This theorem depends on definitions:  df-bi 115  df-tru 1287  df-fal 1290

This theorem is referenced by:  hbnae  1649  sbn  1867  euor  1967  euor2  1999