Theorem 19.41v 1949

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 1572	. 2 |- ( ps -> A. x ps )
2	1	19.41h 1731	1 |- ( E. x ( ph /\ ps ) <-> ( E. x ph /\ ps ) )

Syntax hints:   /\ wa 104   <-> wb 105   E.wex 1538

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-17 1572  ax-ial 1580

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  19.41vv  1950  19.41vvv  1951  19.41vvvv  1952  exdistrv  1957  eeeanv  1984  gencbvex  2847  euxfrdc  2989  euind  2990  dfdif3  3314  r19.9rmv  3583  opabm  4369  eliunxp  4861  relop  4872  dmuni  4933  dmres  5026  dminss  5143  imainss  5144  ssrnres  5171  cnvresima  5218  resco  5233  rnco  5235  coass  5247  xpcom  5275  f11o  5605  fvelrnb  5681  rnoprab  6087  domen  6900  xpassen  6989  genpassl  7711  genpassu  7712