Theorem reximi 2627

Description: Inference quantifying both antecedent and consequent. (Contributed by NM, 18-Oct-1996.)

Hypothesis

Ref	Expression
reximi.1	|- ( ph -> ps )

Assertion

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

Proof of Theorem reximi

Step	Hyp	Ref	Expression
1		reximi.1	. . 3 |- ( ph -> ps )
2	1	a1i 9	. 2 |- ( x e. A -> ( ph -> ps ) )
3	2	reximia 2625	1 |- ( E. x e. A ph -> E. x e. A ps )

Syntax hints:   -> wi 4   e. wcel 2200   E.wrex 2509

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1493  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-4 1556  ax-ial 1580

This theorem depends on definitions:  df-bi 117  df-ral 2513  df-rex 2514

This theorem is referenced by:  rexanaliim  2636  r19.29d2r  2675  r19.35-1  2681  r19.40  2685  reu3  2993  ssiun  4007  iinss  4017  elunirn  5896  tfrcllemssrecs  6504  nnawordex  6683  iinerm  6762  erovlem  6782  xpf1o  7013  fidcenumlemim  7130  omniwomnimkv  7345  genprndl  7719  genprndu  7720  appdiv0nq  7762  ltexprlemm  7798  recexsrlem  7972  rereceu  8087  recexre  8736  aprcl  8804  rexanre  11746  climi2  11814  climi0  11815  climcaucn  11877  prodmodclem2  12103  prodmodc  12104  gcdsupex  12493  gcdsupcl  12494  bezoutlemeu  12543  dfgcd3  12546  isnsgrp  13454  rhmdvdsr  14154  eltg2b  14743  lmcvg  14906  cnptoprest  14928  lmtopcnp  14939  txbas  14947  metrest  15195  elply2  15424  2sqlem7  15815  umgr2edg1  16022  umgr2edgneu  16025  bj-charfunbi  16229  bj-findis  16397