Theorem hbn 1590

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 1589	. 2 |- ( A. x ( ph -> A. x ph ) -> ( -. ph -> A. x -. ph ) )
2		hbn.1	. 2 |- ( ph -> A. x ph )
3	1, 2	mpg 1386	1 |- ( -. ph -> A. x -. ph )

Syntax hints:   -. wn 3   -> wi 4   A.wal 1288

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 580  ax-in2 581  ax-5 1382  ax-gen 1384  ax-ie2 1429  ax-4 1446  ax-ial 1473

This theorem depends on definitions:  df-bi 116  df-tru 1293  df-fal 1296

This theorem is referenced by:  hbnae  1657  sbn  1875  euor  1975  euor2  2007