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Theorem 19.9h 1780
 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.)
Hypothesis
Ref Expression
19.9h.1 (φxφ)
Assertion
Ref Expression
19.9h (xφφ)

Proof of Theorem 19.9h
StepHypRef Expression
1 19.9h.1 . . 3 (φxφ)
21nfi 1551 . 2 xφ
3 19.9t 1779 . 2 (Ⅎxφ → (xφφ))
42, 3ax-mp 5 1 (xφφ)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176  ∀wal 1540  ∃wex 1541  Ⅎwnf 1544 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-11 1746 This theorem depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545 This theorem is referenced by:  19.9  1783  19.23hOLD  1820  cbv3hv  1850
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