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Theorem 19.9 1535
 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 1412 . 2 (𝜑 → ∀𝑥𝜑)
3219.9h 1534 1 (∃𝑥𝜑𝜑)
 Colors of variables: wff set class Syntax hints:   ↔ wb 98  Ⅎwnf 1349  ∃wex 1381 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 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400 This theorem depends on definitions:  df-bi 110  df-nf 1350 This theorem is referenced by:  alexim  1536  19.19  1556  19.36-1  1563  19.44  1572  19.45  1573  19.41  1576
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