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Theorem nf3 1575
Description: An alternative definition of df-nf 1366. (Contributed by Mario Carneiro, 24-Sep-2016.)
Assertion
Ref Expression
nf3 (Ⅎ𝑥𝜑 ↔ ∀𝑥(∃𝑥𝜑𝜑))

Proof of Theorem nf3
StepHypRef Expression
1 nf2 1574 . 2 (Ⅎ𝑥𝜑 ↔ (∃𝑥𝜑 → ∀𝑥𝜑))
2 nfe1 1401 . . . 4 𝑥𝑥𝜑
32nfri 1428 . . 3 (∃𝑥𝜑 → ∀𝑥𝑥𝜑)
4319.21h 1465 . 2 (∀𝑥(∃𝑥𝜑𝜑) ↔ (∃𝑥𝜑 → ∀𝑥𝜑))
51, 4bitr4i 180 1 (Ⅎ𝑥𝜑 ↔ ∀𝑥(∃𝑥𝜑𝜑))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 102  wal 1257  wnf 1365  wex 1397
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-4 1416  ax-ial 1443  ax-i5r 1444
This theorem depends on definitions:  df-bi 114  df-nf 1366
This theorem is referenced by:  eusv2nf  4216
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