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  4425  eliunxp  4921  relop  4932  dmuni  4993  dmres  5086  dminss  5205  imainss  5206  ssrnres  5233  cnvresima  5280  resco  5295  rnco  5297  coass  5309  xpcom  5337  f11o  5676  fvelrnb  5753  rnoprab  6174  domen  7039  xpassen  7132  genpassl  7897  genpassu  7898