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Theorem 19.9t 1515
Description: A closed version of 19.9 1517. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 24-Sep-2016.) (Proof shortended by Wolf Lammen, 30-Dec-2017.)
Assertion
Ref Expression
19.9t (Ⅎxφ → (xφφ))

Proof of Theorem 19.9t
StepHypRef Expression
1 df-nf 1330 . . 3 (Ⅎxφx(φxφ))
2 19.9ht 1514 . . 3 (x(φxφ) → (xφφ))
31, 2sylbi 114 . 2 (Ⅎxφ → (xφφ))
4 19.8a 1464 . 2 (φxφ)
53, 4impbid1 130 1 (Ⅎxφ → (xφφ))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98  wal 1226  wnf 1329  wex 1362
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-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-4 1381
This theorem depends on definitions:  df-bi 110  df-nf 1330
This theorem is referenced by:  19.9d  1533  19.23t  1549  spimt  1606  exdistrfor  1663  sbequi  1702  sbft  1710  vtoclegft  2602  copsexg  3955
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