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Theorem nfim1OLD 1812
 Description: A closed form of nfim 1813. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 24-Sep-2016.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
nfim1.1 xφ
nfim1.2 (φ → Ⅎxψ)
Assertion
Ref Expression
nfim1OLD x(φψ)

Proof of Theorem nfim1OLD
StepHypRef Expression
1 nfim1.2 . . . . 5 (φ → Ⅎxψ)
21nfrd 1763 . . . 4 (φ → (ψxψ))
32a2i 12 . . 3 ((φψ) → (φxψ))
4 nfim1.1 . . . 4 xφ
5419.21 1796 . . 3 (x(φψ) ↔ (φxψ))
63, 5sylibr 203 . 2 ((φψ) → x(φψ))
76nfi 1551 1 x(φψ)
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∀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-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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