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Theorem nf3 1867
Description: An alternative definition of df-nf 1545. (Contributed by Mario Carneiro, 24-Sep-2016.)
Assertion
Ref Expression
nf3 (Ⅎxφx(xφφ))

Proof of Theorem nf3
StepHypRef Expression
1 nf2 1866 . 2 (Ⅎxφ ↔ (xφxφ))
2 nfe1 1732 . . 3 xxφ
3219.21 1796 . 2 (x(xφφ) ↔ (xφxφ))
41, 3bitr4i 243 1 (Ⅎxφx(xφφ))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 176  wal 1540  wex 1541  wnf 1544
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-11 1746
This theorem depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545
This theorem is referenced by: (None)
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