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Theorem 19.9h 2024
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.) (Proof shortened by Wolf Lammen, 5-Jan-2018.) (Proof shortened by Wolf Lammen, 14-Jul-2020.)
Hypothesis
Ref Expression
19.9h.1 (𝜑 → ∀𝑥𝜑)
Assertion
Ref Expression
19.9h (∃𝑥𝜑𝜑)

Proof of Theorem 19.9h
StepHypRef Expression
1 19.9h.1 . . 3 (𝜑 → ∀𝑥𝜑)
21nfi 1703 . 2 𝑥𝜑
3219.9 2023 1 (∃𝑥𝜑𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 191  wal 1466  wex 1692
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1698  ax-4 1711  ax-5 1789  ax-6 1836  ax-7 1883  ax-10 1965  ax-12 1983
This theorem depends on definitions:  df-bi 192  df-ex 1693  df-nf 1697
This theorem is referenced by:  19.9OLD  2028  cbv3hvOLD  2114  cbv3hvOLDOLD  2115  bnj1131  29751  bnj1397  29798
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