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Theorem nfan1 1881
 Description: A closed form of nfan 1824. (Contributed by Mario Carneiro, 3-Oct-2016.)
Hypotheses
Ref Expression
nfan1.1 xφ
nfan1.2 (φ → Ⅎxψ)
Assertion
Ref Expression
nfan1 x(φ ψ)

Proof of Theorem nfan1
StepHypRef Expression
1 nfan1.2 . . . . 5 (φ → Ⅎxψ)
21nfrd 1763 . . . 4 (φ → (ψxψ))
32imdistani 671 . . 3 ((φ ψ) → (φ xψ))
4 nfan1.1 . . . 4 xφ
5419.28 1870 . . 3 (x(φ ψ) ↔ (φ xψ))
63, 5sylibr 203 . 2 ((φ ψ) → x(φ ψ))
76nfi 1551 1 x(φ ψ)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 358  ∀wal 1540  Ⅎwnf 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-11 1746 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-nf 1545 This theorem is referenced by:  spimed  1977  ralcom2  2775  sbcralt  3118  sbcrext  3119  csbiebt  3172
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