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 ) )

This proof depends on syntax axioms:   /\ wa 104   <-> wb 105   E.wex 1545

This proof depends on 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 proof depends on definitions:  df-bi 117

This theorem is used 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  4423  eliunxp  4919  relop  4930  dmuni  4991  dmres  5084  dminss  5202  imainss  5203  ssrnres  5230  cnvresima  5277  resco  5292  rnco  5294  coass  5306  xpcom  5334  f11o  5673  fvelrnb  5750  rnoprab  6171  domen  7035  xpassen  7128  genpassl  7891  genpassu  7892