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Theorem 19.12vv 1898
Description: Special case of 19.12 1847 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 1890 . . 3
21exbii 1582 . 2
3 nfv 1619 . . . 4  F/
43nfal 1842 . . 3  F/
5419.36 1871 . 2
6 19.36v 1896 . . . 4
76albii 1566 . . 3
8 nfv 1619 . . . . 5  F/
98nfal 1842 . . . 4  F/
10919.21 1796 . . 3
117, 10bitr2i 241 . 2
122, 5, 113bitri 262 1
Colors of variables: wff setvar class
Syntax hints:   wi 4   wb 176  wal 1540  wex 1541
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-nf 1545
This theorem is referenced by: (None)
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