Theorem 19.41v 1882

Description: Special case of Theorem 19.41 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.)

Assertion

Ref	Expression
19.41v	|- ( E. x ( ph /\ ps ) <-> ( E. x ph /\ ps ) )

Distinct variable group:   ps, x

Allowed substitution hint:   ph( x)

Proof of Theorem 19.41v

Step	Hyp	Ref	Expression
1		ax-17 1506	. 2 |- ( ps -> A. x ps )
2	1	19.41h 1665	1 |- ( E. x ( ph /\ ps ) <-> ( E. x ph /\ ps ) )

Syntax hints:   /\ wa 103   <-> wb 104   E.wex 1472

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 1427  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-4 1490  ax-17 1506  ax-ial 1514

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  19.41vv  1883  19.41vvv  1884  19.41vvvv  1885  exdistrv  1890  eeeanv  1913  gencbvex  2758  euxfrdc  2898  euind  2899  dfdif3  3218  r19.9rmv  3486  opabm  4242  eliunxp  4727  relop  4738  dmuni  4798  dmres  4889  dminss  5002  imainss  5003  ssrnres  5030  cnvresima  5077  resco  5092  rnco  5094  coass  5106  xpcom  5134  f11o  5449  fvelrnb  5518  rnoprab  5906  domen  6698  xpassen  6777  genpassl  7446  genpassu  7447