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Theorem 19.9h 1531
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.)
Hypothesis
Ref Expression
19.9h.1 (φxφ)
Assertion
Ref Expression
19.9h (xφφ)

Proof of Theorem 19.9h
StepHypRef Expression
1 19.9ht 1529 . . 3 (x(φxφ) → (xφφ))
2 19.9h.1 . . 3 (φxφ)
31, 2mpg 1337 . 2 (xφφ)
4 19.8a 1479 . 2 (φxφ)
53, 4impbii 117 1 (xφφ)
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98  wal 1240  wex 1378
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 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  19.9  1532  excomim  1550  exdistrfor  1678  sbcof2  1688  ax11ev  1706  19.9v  1748  exists1  1993
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