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Theorem 19.42vv 2041
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 2040 . 2  |-  ( E. x E. y (
ph  /\  ps )  <->  E. x ( ph  /\  E. y ps ) )
2 19.42v 2039 . 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  2042  exdistr2  2043  3exdistr  2044  ceqsex3v  2777  ceqsex4v  2778  ceqsex8v  2780  elvvv  4702  dfoprab2  5794  resoprab  5839  oprabex3  5861  ov3  5883  ov6g  5884  xpassen  6889  axaddf  8700  axmulf  8701  brimg  23816  bnj996  27999  dvhopellsm  30437
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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