MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  19.21t Unicode version

Theorem 19.21t 1904
Description: Closed form of Theorem 19.21 of [Margaris] p. 90, see 19.21 1905. (Contributed by NM, 27-May-1997.) (Revised by Mario Carneiro, 24-Sep-2016.) (Proof shortened by Wolf Lammen, 3-Jan-2018.)
Assertion
Ref Expression
19.21t

Proof of Theorem 19.21t
StepHypRef Expression
1 nfr 1873 . . 3
2 alim 1632 . . 3
31, 2syl9 71 . 2
4 19.9t 1890 . . . 4
54imbi1d 317 . . 3
6 19.38 1662 . . 3
75, 6syl6bir 229 . 2
83, 7impbid 191 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  A.wal 1393  E.wex 1612  F/wnf 1616
This theorem is referenced by:  19.21  1905  nfimd  1917  sbal1  2204  sbal2  2205  ax12indalem  2275  ax12inda2ALT  2276  r19.21t  2854  r19.21tOLD  2855  ceqsalt  3132  sbciegft  3358  wl-sbhbt  30002  wl-2sb6d  30008  wl-sbalnae  30012  bj-ceqsalt0  34449  bj-ceqsalt1  34450
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-12 1854
This theorem depends on definitions:  df-bi 185  df-ex 1613  df-nf 1617
  Copyright terms: Public domain W3C validator