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  4006  iinss  4016  elunirn  5889  tfrcllemssrecs  6496  nnawordex  6673  iinerm  6752  erovlem  6772  xpf1o  7001  fidcenumlemim  7115  omniwomnimkv  7330  genprndl  7704  genprndu  7705  appdiv0nq  7747  ltexprlemm  7783  recexsrlem  7957  rereceu  8072  recexre  8721  aprcl  8789  rexanre  11726  climi2  11794  climi0  11795  climcaucn  11857  prodmodclem2  12083  prodmodc  12084  gcdsupex  12473  gcdsupcl  12474  bezoutlemeu  12523  dfgcd3  12526  isnsgrp  13434  rhmdvdsr  14133  eltg2b  14722  lmcvg  14885  cnptoprest  14907  lmtopcnp  14918  txbas  14926  metrest  15174  elply2  15403  2sqlem7  15794  umgr2edg1  16001  umgr2edgneu  16004  bj-charfunbi  16132  bj-findis  16300