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Theorem 19.9h 1579
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 (𝜑 → ∀𝑥𝜑)
Assertion
Ref Expression
19.9h (∃𝑥𝜑𝜑)

Proof of Theorem 19.9h
StepHypRef Expression
1 19.9ht 1577 . . 3 (∀𝑥(𝜑 → ∀𝑥𝜑) → (∃𝑥𝜑𝜑))
2 19.9h.1 . . 3 (𝜑 → ∀𝑥𝜑)
31, 2mpg 1385 . 2 (∃𝑥𝜑𝜑)
4 19.8a 1527 . 2 (𝜑 → ∃𝑥𝜑)
53, 4impbii 124 1 (∃𝑥𝜑𝜑)
Colors of variables: wff set class
Syntax hints:  wi 4  wb 103  wal 1287  wex 1426
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 1383  ax-ie1 1427  ax-ie2 1428  ax-4 1445
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  19.9  1580  excomim  1598  exdistrfor  1728  sbcof2  1738  ax11ev  1756  19.9v  1799  exists1  2044
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