Theorem hbnOLD 1706

Description: Obsolete proof of hbn 1703 as of 2-May-2026. (Contributed by NM, 5-Aug-1993.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

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

Assertion

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

Proof of Theorem hbnOLD

Step	Hyp	Ref	Expression
1		hbnt 1705	. 2 |- ( A. x ( ph -> A. x ph ) -> ( -. ph -> A. x -. ph ) )
2		hbnOLD.1	. 2 |- ( ph -> A. x ph )
3	1, 2	mpg 1504	1 |- ( -. ph -> A. x -. ph )

This proof depends on syntax axioms:   -. wn 3   -> wi 4   A.wal 1400

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 623  ax-in2 624  ax-5 1500  ax-gen 1502  ax-ie2 1547  ax-4 1563  ax-ial 1587

This proof depends on definitions:  df-bi 117  df-tru 1405  df-fal 1408

This theorem is used by: (None)