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Theorem 19.9 1578
Description: A wff may be existentially quantified with a variable not free in it. Theorem 19.9 of [Margaris] p. 89. (Contributed by FL, 24-Mar-2007.) (Revised by Mario Carneiro, 24-Sep-2016.) (Proof shortened by Wolf Lammen, 30-Dec-2017.)
Hypothesis
Ref Expression
19.9.1  |-  F/ x ph
Assertion
Ref Expression
19.9  |-  ( E. x ph  <->  ph )

Proof of Theorem 19.9
StepHypRef Expression
1 19.9.1 . . 3  |-  F/ x ph
21nfri 1455 . 2  |-  ( ph  ->  A. x ph )
3219.9h 1577 1  |-  ( E. x ph  <->  ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 103   F/wnf 1392   E.wex 1424
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-4 1443
This theorem depends on definitions:  df-bi 115  df-nf 1393
This theorem is referenced by:  alexim  1579  19.19  1599  19.36-1  1606  19.44  1615  19.45  1616  19.41  1619
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