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Theorem 19.12vv 1986
Description: Special case of 19.12 1950 where its converse holds. See 19.12vvv 1765 for a version with a dv condition requiring fewer axioms. (Contributed by NM, 18-Jul-2001.) (Revised by Andrew Salmon, 11-Jul-2011.)
Assertion
Ref Expression
19.12vv
Distinct variable groups:   ,   ,

Proof of Theorem 19.12vv
StepHypRef Expression
1 19.21v 1729 . . 3
21exbii 1667 . 2
3 nfv 1707 . . . 4
43nfal 1947 . . 3
5419.36 1964 . 2
6 19.36v 1762 . . . 4
76albii 1640 . . 3
8 nfv 1707 . . . . 5
98nfal 1947 . . . 4
10919.21 1905 . . 3
117, 10bitr2i 250 . 2
122, 5, 113bitri 271 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  A.wal 1393  E.wex 1612
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-11 1842  ax-12 1854
This theorem depends on definitions:  df-bi 185  df-ex 1613  df-nf 1617
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