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Theorem nf3 1680
Description: An alternate definition of df-nf 1472. (Contributed by Mario Carneiro, 24-Sep-2016.)
Assertion
Ref Expression
nf3 (Ⅎ𝑥𝜑 ↔ ∀𝑥(∃𝑥𝜑𝜑))

Proof of Theorem nf3
StepHypRef Expression
1 nf2 1679 . 2 (Ⅎ𝑥𝜑 ↔ (∃𝑥𝜑 → ∀𝑥𝜑))
2 nfe1 1507 . . . 4 𝑥𝑥𝜑
32nfri 1530 . . 3 (∃𝑥𝜑 → ∀𝑥𝑥𝜑)
4319.21h 1568 . 2 (∀𝑥(∃𝑥𝜑𝜑) ↔ (∃𝑥𝜑 → ∀𝑥𝜑))
51, 4bitr4i 187 1 (Ⅎ𝑥𝜑 ↔ ∀𝑥(∃𝑥𝜑𝜑))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 105  wal 1362  wnf 1471  wex 1503
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1458  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-4 1521  ax-ial 1545  ax-i5r 1546
This theorem depends on definitions:  df-bi 117  df-nf 1472
This theorem is referenced by:  hbe1a  2035  eusv2nf  4477
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