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Theorem 19.37v 1834
Description: Version of 19.37 2065 with a dv condition, requiring fewer axioms. (Contributed by NM, 21-Jun-1993.)
Assertion
Ref Expression
19.37v  |-  ( E. x ( ph  ->  ps )  <->  ( ph  ->  E. x ps ) )
Distinct variable group:    ph, x
Allowed substitution hint:    ps( x)

Proof of Theorem 19.37v
StepHypRef Expression
1 19.35 1748 . 2  |-  ( E. x ( ph  ->  ps )  <->  ( A. x ph  ->  E. x ps )
)
2 19.3v 1821 . . 3  |-  ( A. x ph  <->  ph )
32imbi1i 332 . 2  |-  ( ( A. x ph  ->  E. x ps )  <->  ( ph  ->  E. x ps )
)
41, 3bitri 257 1  |-  ( E. x ( ph  ->  ps )  <->  ( ph  ->  E. x ps ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 189   A.wal 1450   E.wex 1671
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813
This theorem depends on definitions:  df-bi 190  df-ex 1672
This theorem is referenced by:  19.37iv  1835  axrep5  4513  fvn0ssdmfun  6028  kmlem14  8611  kmlem15  8612  eqvincg  28189  bnj132  29604  bnj1098  29667  bnj150  29759  bnj865  29806  bnj996  29838  bnj1021  29847  bnj1090  29860  bnj1176  29886  bj-axrep5  31473  cnvssco  36283  refimssco  36284  19.37vv  36804  pm11.61  36813  relopabVD  37361  rmoanim  38745
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