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Theorem 19.9h 2106
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 2011 . 2 𝑥𝜑
3219.9 2060 1 (∃𝑥𝜑𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 195  wal 1473  wex 1695
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-12 2034
This theorem depends on definitions:  df-bi 196  df-ex 1696  df-nf 1701
This theorem is referenced by:  cbv3hvOLD  2161  cbv3hvOLDOLD  2162  bnj1131  30112  bnj1397  30159
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