Theorem exim 1714

Description: Theorem 19.22 of [Margaris] p. 90. (Contributed by NM, 10-Jan-1993.) (Proof shortened by Wolf Lammen, 4-Jul-2014.)

Assertion

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

Proof of Theorem exim

Step	Hyp	Ref	Expression
1		id 22	. 2 |- ( ( ph -> ps ) -> ( ph -> ps ) )
2	1	aleximi 1712	1 |- ( A. x ( ph -> ps ) -> ( E. x ph -> E. x ps ) )

Syntax hints:   -> wi 4   A.wal 1450   E.wex 1671

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690

This theorem depends on definitions:  df-bi 190  df-ex 1672

This theorem is referenced by:  eximi  1715  19.23v  1826  19.8a  1955  19.8aOLD  1956  19.9ht  1987  19.23tOLD  2012  spimt  2110  elex2  3044  elex22  3045  vtoclegft  3107  spcimgft  3111  bj-axdd2  31239  bj-2exim  31267  bj-exlimh  31275  bj-sbex  31303  bj-alequex  31375  bj-spimtv  31385  bj-spcimdv  31561  2exim  36798  pm11.71  36817  onfrALTlem2  36982  19.41rg  36987  ax6e2nd  36995  elex2VD  37297  elex22VD  37298  onfrALTlem2VD  37349  19.41rgVD  37362  ax6e2eqVD  37367  ax6e2ndVD  37368  ax6e2ndeqVD  37369  ax6e2ndALT  37390  ax6e2ndeqALT  37391