Theorem hbim1 1563

Description: A closed form of hbim 1538. (Contributed by NM, 5-Aug-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 11	. 2 |- ( ( ph -> ps ) -> ( ph -> A. x ps ) )
3		hbim1.1	. . 3 |- ( ph -> A. x ph )
4	3	19.21h 1550	. 2 |- ( A. x ( ph -> ps ) <-> ( ph -> A. x ps ) )
5	2, 4	sylibr 133	1 |- ( ( ph -> ps ) -> A. x ( ph -> ps ) )

Syntax hints:   -> wi 4   A.wal 1346

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1440  ax-gen 1442  ax-4 1503  ax-ial 1527  ax-i5r 1528

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  nfim1  1564  sbco2d  1959  sbco2vd  1960