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Theorem 19.12 1950
Description: Theorem 19.12 of [Margaris] p. 89. Assuming the converse is a mistake sometimes made by beginners! But sometimes the converse does hold, as in 19.12vv 1986 and r19.12sn 4095. (Contributed by NM, 12-Mar-1993.) (Proof shortened by Wolf Lammen, 3-Jan-2018.)
Assertion
Ref Expression
19.12

Proof of Theorem 19.12
StepHypRef Expression
1 nfa1 1897 . . 3
21nfex 1948 . 2
3 sp 1859 . . 3
43eximi 1656 . 2
52, 4alrimi 1877 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  A.wal 1393  E.wex 1612
This theorem is referenced by:  pm11.61  31299
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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