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Theorem nfnfOLD 1846
 Description: Obsolete proof of nfnf 1845 as of 30-Dec-2017. (Contributed by Mario Carneiro, 11-Aug-2016.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
nfal.1 xφ
Assertion
Ref Expression
nfnfOLD xyφ

Proof of Theorem nfnfOLD
StepHypRef Expression
1 df-nf 1545 . 2 (Ⅎyφy(φyφ))
2 nfal.1 . . . . . 6 xφ
32a1i 10 . . . . 5 ( ⊤ → Ⅎxφ)
42nfal 1842 . . . . . 6 xyφ
54a1i 10 . . . . 5 ( ⊤ → Ⅎxyφ)
63, 5nfimd 1808 . . . 4 ( ⊤ → Ⅎx(φyφ))
76trud 1323 . . 3 x(φyφ)
87nfal 1842 . 2 xy(φyφ)
91, 8nfxfr 1570 1 xyφ
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ⊤ wtru 1316  ∀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-7 1734  ax-11 1746 This theorem depends on definitions:  df-bi 177  df-tru 1319  df-ex 1542  df-nf 1545 This theorem is referenced by: (None)
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