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Theorem 19.9h 2283
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)
21nf5i 2179 . 2 𝑥𝜑
3219.9 2228 1 (∃𝑥𝜑𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  wal 1629  wex 1852
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885  ax-5 1991  ax-6 2057  ax-7 2093  ax-10 2174  ax-12 2203
This theorem depends on definitions:  df-bi 197  df-ex 1853  df-nf 1858
This theorem is referenced by:  bnj1131  31196  bnj1397  31243
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