Theorem exim 1706

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 1704	1 |- ( A. x ( ph -> ps ) -> ( E. x ph -> E. x ps ) )

Syntax hints:   -> wi 4   A.wal 1442   E.wex 1663

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682

This theorem depends on definitions:  df-bi 189  df-ex 1664

This theorem is referenced by:  eximi  1707  19.23v  1818  19.8a  1935  19.8aOLD  1936  19.9ht  1967  19.23tOLD  1992  spimt  2097  elex2  3058  elex22  3059  vtoclegft  3121  spcimgft  3125  bj-axdd2  31175  bj-2exim  31203  bj-exlimh  31211  bj-sbex  31239  bj-alequex  31309  bj-spimtv  31319  bj-spcimdv  31493  wl-19.8a  31910  2exim  36728  pm11.71  36747  onfrALTlem2  36912  19.41rg  36917  ax6e2nd  36925  elex2VD  37234  elex22VD  37235  onfrALTlem2VD  37286  19.41rgVD  37299  ax6e2eqVD  37304  ax6e2ndVD  37305  ax6e2ndeqVD  37306  ax6e2ndALT  37327  ax6e2ndeqALT  37328