Theorem hbn 1665

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 1664	. 2 |- ( A. x ( ph -> A. x ph ) -> ( -. ph -> A. x -. ph ) )
2		hbn.1	. 2 |- ( ph -> A. x ph )
3	1, 2	mpg 1462	1 |- ( -. ph -> A. x -. ph )

Syntax hints:   -. wn 3   -> wi 4   A.wal 1362

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616  ax-5 1458  ax-gen 1460  ax-ie2 1505  ax-4 1521  ax-ial 1545

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-fal 1370

This theorem is referenced by:  hbnae  1732  sbn  1964  euor  2064  euor2  2096