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Theorem nfan1 1438
Description: A closed form of nfan 1439. (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 1394 . . . 4 (φ → (ψxψ))
32imdistani 422 . . 3 ((φ ψ) → (φ xψ))
4 nfan1.1 . . . . 5 xφ
54nfri 1393 . . . 4 (φxφ)
6519.28h 1436 . . 3 (x(φ ψ) ↔ (φ xψ))
73, 6sylibr 137 . 2 ((φ ψ) → x(φ ψ))
87nfi 1331 1 x(φ ψ)
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97  wal 1226  wnf 1329
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1316  ax-gen 1318  ax-4 1381
This theorem depends on definitions:  df-bi 110  df-nf 1330
This theorem is referenced by:  nfan  1439  sbcralt  2811  sbcrext  2812  csbiebt  2863  riota5f  5416
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