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Theorem 19.9 1513
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 xφ
Assertion
Ref Expression
19.9 (xφφ)

Proof of Theorem 19.9
StepHypRef Expression
1 19.9.1 . . 3 xφ
21nfri 1389 . 2 (φxφ)
3219.9h 1512 1 (xφφ)
Colors of variables: wff set class
Syntax hints:  wb 98  wnf 1325  wex 1358
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-gen 1314  ax-ie1 1359  ax-ie2 1360  ax-4 1377
This theorem depends on definitions:  df-bi 110  df-nf 1326
This theorem is referenced by:  alexim  1514  19.19  1534  19.36-1  1541  19.44  1550  19.45  1551  19.41  1554
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