Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  19.12vv Structured version   Unicode version

Theorem 19.12vv 1925
 Description: Special case of 19.12 1872 where its converse holds. (Contributed by NM, 18-Jul-2001.) (Revised by Andrew Salmon, 11-Jul-2011.)
Assertion
Ref Expression
19.12vv
Distinct variable groups:   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem 19.12vv
StepHypRef Expression
1 19.21v 1917 . . 3
21exbii 1593 . 2
3 nfv 1631 . . . 4
43nfal 1867 . . 3
5419.36 1896 . 2
6 19.36v 1923 . . . 4
76albii 1576 . . 3
8 nfv 1631 . . . . 5
98nfal 1867 . . . 4
10919.21 1817 . . 3
117, 10bitr2i 243 . 2
122, 5, 113bitri 264 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178  wal 1550  wex 1551 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1628  ax-9 1669  ax-8 1690  ax-6 1747  ax-7 1752  ax-11 1764 This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1552  df-nf 1555
 Copyright terms: Public domain W3C validator