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Theorem nf6 2282
Description: An alternate definition of df-nf 1776. (Contributed by Mario Carneiro, 24-Sep-2016.)
Assertion
Ref Expression
nf6 (Ⅎ𝑥𝜑 ↔ ∀𝑥(∃𝑥𝜑𝜑))

Proof of Theorem nf6
StepHypRef Expression
1 df-nf 1776 . 2 (Ⅎ𝑥𝜑 ↔ (∃𝑥𝜑 → ∀𝑥𝜑))
2 nfe1 2145 . . 3 𝑥𝑥𝜑
3219.21 2197 . 2 (∀𝑥(∃𝑥𝜑𝜑) ↔ (∃𝑥𝜑 → ∀𝑥𝜑))
41, 3bitr4i 279 1 (Ⅎ𝑥𝜑 ↔ ∀𝑥(∃𝑥𝜑𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 207  wal 1526  wex 1771  wnf 1775
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-10 2136  ax-12 2167
This theorem depends on definitions:  df-bi 208  df-ex 1772  df-nf 1776
This theorem is referenced by:  eusv2nf  5286  xfree  30148
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