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Theorem 19.42vv 1848
Description: Theorem 19.42 of [Margaris] p. 90 with 2 quantifiers. (Contributed by NM, 16-Mar-1995.)
Assertion
Ref Expression
19.42vv  |-  ( E. x E. y (
ph  /\  ps )  <->  (
ph  /\  E. x E. y ps ) )
Distinct variable groups:    ph, x    ph, y
Allowed substitution hints:    ps( x, y)

Proof of Theorem 19.42vv
StepHypRef Expression
1 exdistr 1847 . 2  |-  ( E. x E. y (
ph  /\  ps )  <->  E. x ( ph  /\  E. y ps ) )
2 19.42v 1846 . 2  |-  ( E. x ( ph  /\  E. y ps )  <->  ( ph  /\ 
E. x E. y ps ) )
31, 2bitri 240 1  |-  ( E. x E. y (
ph  /\  ps )  <->  (
ph  /\  E. x E. y ps ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    /\ wa 358   E.wex 1528
This theorem is referenced by:  19.42vvv  1849  exdistr2  1850  3exdistr  1851  ceqsex3v  2826  ceqsex4v  2827  ceqsex8v  2829  elvvv  4749  dfoprab2  5895  resoprab  5940  oprabex3  5962  ov3  5984  ov6g  5985  xpassen  6956  axaddf  8767  axmulf  8768  brimg  24476  bnj996  28987  dvhopellsm  31307
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
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