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Theorem 19.12vv 1921
 Description: Special case of 19.12 1869 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 1913 . . 3
21exbii 1592 . 2
3 nfv 1629 . . . 4
43nfal 1864 . . 3
5419.36 1892 . 2
6 19.36v 1919 . . . 4
76albii 1575 . . 3
8 nfv 1629 . . . . 5
98nfal 1864 . . . 4
10919.21 1814 . . 3
117, 10bitr2i 242 . 2
122, 5, 113bitri 263 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177  wal 1549  wex 1550 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761 This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-nf 1554
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