Theorem 19.41v 1958

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 1579	. 2 |- ( ps -> A. x ps )
2	1	19.41h 1737	1 |- ( E. x ( ph /\ ps ) <-> ( E. x ph /\ ps ) )

Syntax hints:   /\ wa 104   <-> wb 105   E.wex 1545

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 1500  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-4 1563  ax-17 1579  ax-ial 1587

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  19.41vv  1959  19.41vvv  1960  19.41vvvv  1961  exdistrv  1966  eeeanv  1993  gencbvex  2869  euxfrdc  3012  euind  3013  dfdif3  3339  r19.9rmv  3619  opabm  4421  eliunxp  4917  relop  4928  dmuni  4989  dmres  5082  dminss  5200  imainss  5201  ssrnres  5228  cnvresima  5275  resco  5290  rnco  5292  coass  5304  xpcom  5332  f11o  5671  fvelrnb  5747  rnoprab  6164  domen  7028  xpassen  7121  genpassl  7884  genpassu  7885