Theorem hbntOLD 2145

Description: Obsolete proof of hbnt 2144 as of 13-Oct-2021. (Contributed by NM, 10-May-1993.) (Proof shortened by Wolf Lammen, 3-Mar-2018.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

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

Proof of Theorem hbntOLD

Step	Hyp	Ref	Expression
1		df-ex 1705	. . 3 |- ( E. x ph <-> -. A. x -. ph )
2		19.9ht 2143	. . 3 |- ( A. x ( ph -> A. x ph ) -> ( E. x ph -> ph ) )
3	1, 2	syl5bir 233	. 2 |- ( A. x ( ph -> A. x ph ) -> ( -. A. x -. ph -> ph ) )
4	3	con1d 139	1 |- ( A. x ( ph -> A. x ph ) -> ( -. ph -> A. x -. ph ) )

Syntax hints:   -. wn 3   -> wi 4   A.wal 1481   E.wex 1704

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-10 2019  ax-12 2047

This theorem depends on definitions:  df-bi 197  df-ex 1705

This theorem is referenced by: (None)