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  2848  euxfrdc  2990  euind  2991  dfdif3  3315  r19.9rmv  3584  opabm  4373  eliunxp  4867  relop  4878  dmuni  4939  dmres  5032  dminss  5149  imainss  5150  ssrnres  5177  cnvresima  5224  resco  5239  rnco  5241  coass  5253  xpcom  5281  f11o  5613  fvelrnb  5689  rnoprab  6099  domen  6917  xpassen  7009  genpassl  7734  genpassu  7735