Theorem eeanv 1988

Description: Rearrange existential quantifiers. (Contributed by NM, 26-Jul-1995.)

Assertion

Ref	Expression
eeanv	|- ( E. x E. y ( ph /\ ps ) <-> ( E. x ph /\ E. y ps ) )

Distinct variable groups:   ph, y   ps, x

Allowed substitution hints:   ph( x)   ps( y)

Proof of Theorem eeanv

Step	Hyp	Ref	Expression
1		nfv 1577	. 2 |- F/ y ph
2		nfv 1577	. 2 |- F/ x ps
3	1, 2	eean 1987	1 |- ( E. x E. y ( ph /\ ps ) <-> ( E. x ph /\ E. y ps ) )

Syntax hints:   /\ wa 104   <-> wb 105   E.wex 1541

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 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-4 1559  ax-17 1575  ax-ial 1583

This theorem depends on definitions:  df-bi 117  df-nf 1510

This theorem is referenced by:  eeeanv  1989  ee4anv  1990  2eu4  2176  cgsex2g  2852  cgsex4g  2853  vtocl2  2872  spc2egv  2909  spc2gv  2910  dtruarb  4306  copsex2t  4363  copsex2g  4364  opelopabsb  4380  xpmlem  5185  fununi  5426  imain  5440  brabvv  6101  spc2ed  6431  tfrlem7  6550  ener  7021  domtr  7027  unen  7060  mapen  7101  sbthlemi10  7238  ltexprlemdisj  7923  recexprlemdisj  7947  hashfacen  11212  summodc  12073