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Theorem 19.42vv 1931
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 1930 . 2  |-  ( E. x E. y (
ph  /\  ps )  <->  E. x ( ph  /\  E. y ps ) )
2 19.42v 1929 . 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 1551
This theorem is referenced by:  19.42vvv  1932  exdistr2  1933  3exdistr  1934  ceqsex3v  2996  ceqsex4v  2997  ceqsex8v  2999  elvvv  4939  dfoprab2  6123  resoprab  6168  oprabex3  6190  ov3  6212  ov6g  6213  xpassen  7204  axaddf  9022  axmulf  9023  usgraedg4  21408  qqhval2  24368  el2wlkonot  28389  el2spthonot  28390  el2wlkonotot0  28392  bnj996  29388  dvhopellsm  31977
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-11 1762
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1552  df-nf 1555
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