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Theorem 19.9h 1516
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 1514 . . 3 (x(φxφ) → (xφφ))
2 19.9h.1 . . 3 (φxφ)
31, 2mpg 1320 . 2 (xφφ)
4 19.8a 1464 . 2 (φxφ)
53, 4impbii 117 1 (xφφ)
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98  wal 1226  wex 1362
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 1318  ax-ie1 1363  ax-ie2 1364  ax-4 1381
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  19.9  1517  excomim  1535  exdistrfor  1663  sbcof2  1673  ax11ev  1691  19.9v  1733  exists1  1978
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