Theorem hbim1 2125

Description: A closed form of hbim 2127. (Contributed by NM, 2-Jun-1993.)

Hypotheses

Ref	Expression
hbim1.1	|- ( ph -> A. x ph )
hbim1.2	|- ( ph -> ( ps -> A. x ps ) )

Assertion

Ref	Expression
hbim1	|- ( ( ph -> ps ) -> A. x ( ph -> ps ) )

Proof of Theorem hbim1

Step	Hyp	Ref	Expression
1		hbim1.2	. . 3 |- ( ph -> ( ps -> A. x ps ) )
2	1	a2i 14	. 2 |- ( ( ph -> ps ) -> ( ph -> A. x ps ) )
3		hbim1.1	. . 3 |- ( ph -> A. x ph )
4	3	19.21h 2121	. 2 |- ( A. x ( ph -> ps ) <-> ( ph -> A. x ps ) )
5	2, 4	sylibr 224	1 |- ( ( ph -> ps ) -> A. x ( ph -> ps ) )

Syntax hints:   -> 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  df-nf 1710

This theorem is referenced by:  hbim  2127  axc14  2372