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Theorem 19.37 1894
Description: Theorem 19.37 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
19.37.1  |-  F/ x ph
Assertion
Ref Expression
19.37  |-  ( E. x ( ph  ->  ps )  <->  ( ph  ->  E. x ps ) )

Proof of Theorem 19.37
StepHypRef Expression
1 19.35 1610 . 2  |-  ( E. x ( ph  ->  ps )  <->  ( A. x ph  ->  E. x ps )
)
2 19.37.1 . . . 4  |-  F/ x ph
3219.3 1791 . . 3  |-  ( A. x ph  <->  ph )
43imbi1i 316 . 2  |-  ( ( A. x ph  ->  E. x ps )  <->  ( ph  ->  E. x ps )
)
51, 4bitri 241 1  |-  ( E. x ( ph  ->  ps )  <->  ( ph  ->  E. x ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 177   A.wal 1549   E.wex 1550   F/wnf 1553
This theorem is referenced by:  19.37v  1922  bnj900  29052
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-11 1761
This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-nf 1554
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