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Theorem nfalt 1467
 Description: Closed form of nfal 1465. (Contributed by Jim Kingdon, 11-May-2018.)
Assertion
Ref Expression
nfalt (yxφ → Ⅎxyφ)

Proof of Theorem nfalt
StepHypRef Expression
1 alim 1343 . . . 4 (y(φxφ) → (yφyxφ))
2 alcom 1364 . . . 4 (yxφxyφ)
31, 2syl6ib 150 . . 3 (y(φxφ) → (yφxyφ))
43alimi 1341 . 2 (xy(φxφ) → x(yφxyφ))
5 df-nf 1347 . . . 4 (Ⅎxφx(φxφ))
65albii 1356 . . 3 (yxφyx(φxφ))
7 alcom 1364 . . 3 (yx(φxφ) ↔ xy(φxφ))
86, 7bitri 173 . 2 (yxφxy(φxφ))
9 df-nf 1347 . 2 (Ⅎxyφx(yφxyφ))
104, 8, 93imtr4i 190 1 (yxφ → Ⅎxyφ)
 Colors of variables: wff set class Syntax hints:   → wi 4  ∀wal 1240  Ⅎwnf 1346 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 1333  ax-7 1334  ax-gen 1335 This theorem depends on definitions:  df-bi 110  df-nf 1347 This theorem is referenced by:  dvelimor  1891
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