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Theorem nf6 2292
Description: An alternate definition of df-nf 1864. (Contributed by Mario Carneiro, 24-Sep-2016.)
Assertion
Ref Expression
nf6 (Ⅎ𝑥𝜑 ↔ ∀𝑥(∃𝑥𝜑𝜑))

Proof of Theorem nf6
StepHypRef Expression
1 df-nf 1864 . 2 (Ⅎ𝑥𝜑 ↔ (∃𝑥𝜑 → ∀𝑥𝜑))
2 nfe1 2194 . . 3 𝑥𝑥𝜑
3219.21 2242 . 2 (∀𝑥(∃𝑥𝜑𝜑) ↔ (∃𝑥𝜑 → ∀𝑥𝜑))
41, 3bitr4i 269 1 (Ⅎ𝑥𝜑 ↔ ∀𝑥(∃𝑥𝜑𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 197  wal 1635  wex 1859  wnf 1863
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1877  ax-4 1894  ax-5 2001  ax-6 2068  ax-7 2104  ax-10 2185  ax-12 2214
This theorem depends on definitions:  df-bi 198  df-ex 1860  df-nf 1864
This theorem is referenced by:  eusv2nf  5062  xfree  29629
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