Theorem 19.42v 1899

Description: Special case of Theorem 19.42 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.)

Assertion

Ref	Expression
19.42v	|- ( E. x ( ph /\ ps ) <-> ( ph /\ E. x ps ) )

Distinct variable group:   ph, x

Allowed substitution hint:   ps( x)

Proof of Theorem 19.42v

Step	Hyp	Ref	Expression
1		ax-17 1519	. 2 |- ( ph -> A. x ph )
2	1	19.42h 1680	1 |- ( E. x ( ph /\ ps ) <-> ( ph /\ E. x ps ) )

Syntax hints:   /\ wa 103   <-> wb 104   E.wex 1485

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1440  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-4 1503  ax-17 1519  ax-ial 1527

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  exdistr  1902  19.42vv  1904  19.42vvv  1905  4exdistr  1909  cbvex2  1915  2sb5  1976  2sb5rf  1982  rexcom4a  2754  ceqsex2  2770  reuind  2935  2rmorex  2936  sbccomlem  3029  bm1.3ii  4110  opm  4219  eqvinop  4228  uniuni  4436  elco  4777  dmopabss  4823  dmopab3  4824  mptpreima  5104  brprcneu  5489  relelfvdm  5528  fndmin  5603  fliftf  5778  dfoprab2  5900  dmoprab  5934  dmoprabss  5935  fnoprabg  5954  opabex3d  6100  opabex3  6101  eroveu  6604  dmaddpq  7341  dmmulpq  7342  prarloc  7465  ltexprlemopl  7563  ltexprlemlol  7564  ltexprlemopu  7565  ltexprlemupu  7566  shftdm  10786  ntreq0  12926  bdbm1.3ii  13926