Theorem 19.41v 1951

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 1574	. 2 |- ( ps -> A. x ps )
2	1	19.41h 1733	1 |- ( E. x ( ph /\ ps ) <-> ( E. x ph /\ ps ) )

Syntax hints:   /\ wa 104   <-> wb 105   E.wex 1540

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 1495  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-4 1558  ax-17 1574  ax-ial 1582

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  19.41vv  1952  19.41vvv  1953  19.41vvvv  1954  exdistrv  1959  eeeanv  1986  gencbvex  2850  euxfrdc  2992  euind  2993  dfdif3  3317  r19.9rmv  3586  opabm  4375  eliunxp  4869  relop  4880  dmuni  4941  dmres  5034  dminss  5151  imainss  5152  ssrnres  5179  cnvresima  5226  resco  5241  rnco  5243  coass  5255  xpcom  5283  f11o  5617  fvelrnb  5693  rnoprab  6103  domen  6921  xpassen  7013  genpassl  7743  genpassu  7744