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Theorem nf3 1632
Description: An alternate definition of df-nf 1422. (Contributed by Mario Carneiro, 24-Sep-2016.)
Assertion
Ref Expression
nf3 (Ⅎ𝑥𝜑 ↔ ∀𝑥(∃𝑥𝜑𝜑))

Proof of Theorem nf3
StepHypRef Expression
1 nf2 1631 . 2 (Ⅎ𝑥𝜑 ↔ (∃𝑥𝜑 → ∀𝑥𝜑))
2 nfe1 1457 . . . 4 𝑥𝑥𝜑
32nfri 1484 . . 3 (∃𝑥𝜑 → ∀𝑥𝑥𝜑)
4319.21h 1521 . 2 (∀𝑥(∃𝑥𝜑𝜑) ↔ (∃𝑥𝜑 → ∀𝑥𝜑))
51, 4bitr4i 186 1 (Ⅎ𝑥𝜑 ↔ ∀𝑥(∃𝑥𝜑𝜑))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 104  wal 1314  wnf 1421  wex 1453
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1408  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-4 1472  ax-ial 1499  ax-i5r 1500
This theorem depends on definitions:  df-bi 116  df-nf 1422
This theorem is referenced by:  eusv2nf  4347
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