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Theorem 19.42vv 2040
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 2039 . 2  |-  ( E. x E. y (
ph  /\  ps )  <->  E. x ( ph  /\  E. y ps ) )
2 19.42v 2038 . 2  |-  ( E. x ( ph  /\  E. y ps )  <->  ( ph  /\ 
E. x E. y ps ) )
31, 2bitri 242 1  |-  ( E. x E. y (
ph  /\  ps )  <->  (
ph  /\  E. x E. y ps ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 178    /\ wa 360   E.wex 1537
This theorem is referenced by:  19.42vvv  2041  exdistr2  2042  3exdistr  2043  ceqsex3v  2764  ceqsex4v  2765  ceqsex8v  2767  elvvv  4656  dfoprab2  5747  resoprab  5792  oprabex3  5814  ov3  5836  ov6g  5837  xpassen  6841  axaddf  8647  axmulf  8648  brimg  23650  bnj996  27676  dvhopellsm  29996
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-gen 1536  ax-17 1628  ax-4 1692
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1538  df-nf 1540
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