Theorem hbntg 31711

Description: A more general form of hbnt 2144. (Contributed by Scott Fenton, 13-Dec-2010.)

Assertion

Ref	Expression
hbntg	|- ( A. x ( ph -> A. x ps ) -> ( -. ps -> A. x -. ph ) )

Proof of Theorem hbntg

Step	Hyp	Ref	Expression
1		axc7 2132	. . 3 |- ( -. A. x -. A. x ps -> ps )
2	1	con1i 144	. 2 |- ( -. ps -> A. x -. A. x ps )
3		con3 149	. . 3 |- ( ( ph -> A. x ps ) -> ( -. A. x ps -> -. ph ) )
4	3	al2imi 1743	. 2 |- ( A. x ( ph -> A. x ps ) -> ( A. x -. A. x ps -> A. x -. ph ) )
5	2, 4	syl5 34	1 |- ( A. x ( ph -> A. x ps ) -> ( -. ps -> A. x -. ph ) )

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

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:  hbimtg  31712  hbng  31714