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Theorem 19.9h 2117
 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 2021 . 2 𝑥𝜑
3219.9 2070 1 (∃𝑥𝜑𝜑)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 196  ∀wal 1478  ∃wex 1701 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-10 2016  ax-12 2044 This theorem depends on definitions:  df-bi 197  df-ex 1702  df-nf 1707 This theorem is referenced by:  cbv3hvOLD  2172  cbv3hvOLDOLD  2173  bnj1131  30619  bnj1397  30666
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