MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  19.41vv Unicode version

Theorem 19.41vv 1843
Description: Theorem 19.41 of [Margaris] p. 90 with 2 quantifiers. (Contributed by NM, 30-Apr-1995.)
Assertion
Ref Expression
19.41vv  |-  ( E. x E. y (
ph  /\  ps )  <->  ( E. x E. y ph  /\  ps ) )
Distinct variable groups:    ps, x    ps, y
Allowed substitution hints:    ph( x, y)

Proof of Theorem 19.41vv
StepHypRef Expression
1 19.41v 1842 . . 3  |-  ( E. y ( ph  /\  ps )  <->  ( E. y ph  /\  ps ) )
21exbii 1569 . 2  |-  ( E. x E. y (
ph  /\  ps )  <->  E. x ( E. y ph  /\  ps ) )
3 19.41v 1842 . 2  |-  ( E. x ( E. y ph  /\  ps )  <->  ( E. x E. y ph  /\  ps ) )
42, 3bitri 240 1  |-  ( E. x E. y (
ph  /\  ps )  <->  ( E. x E. y ph  /\  ps ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    /\ wa 358   E.wex 1528
This theorem is referenced by:  19.41vvv  1844  pm11.07  2054  rabxp  4725  mpt2mptx  5938  copsex2gb  6180  xpassen  6956  dfac5lem1  7750  dfdm5  24132  dfrn5  24133  brtxp2  24421  brpprod3a  24426  brimg  24476  brsuccf  24480  dfoprab4pop  25037  bnj996  28987  diblsmopel  31361
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-11 1715
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1529  df-nf 1532
  Copyright terms: Public domain W3C validator