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Theorem nf6 2260
Description: An alternate definition of df-nf 1855. (Contributed by Mario Carneiro, 24-Sep-2016.)
Assertion
Ref Expression
nf6 (Ⅎ𝑥𝜑 ↔ ∀𝑥(∃𝑥𝜑𝜑))

Proof of Theorem nf6
StepHypRef Expression
1 df-nf 1855 . 2 (Ⅎ𝑥𝜑 ↔ (∃𝑥𝜑 → ∀𝑥𝜑))
2 nfe1 2172 . . 3 𝑥𝑥𝜑
3219.21 2218 . 2 (∀𝑥(∃𝑥𝜑𝜑) ↔ (∃𝑥𝜑 → ∀𝑥𝜑))
41, 3bitr4i 267 1 (Ⅎ𝑥𝜑 ↔ ∀𝑥(∃𝑥𝜑𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  wal 1626  wex 1849  wnf 1853
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1867  ax-4 1882  ax-5 1984  ax-6 2050  ax-7 2086  ax-10 2164  ax-12 2192
This theorem depends on definitions:  df-bi 197  df-ex 1850  df-nf 1855
This theorem is referenced by:  eusv2nf  5009  xfree  29608
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