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Theorem 19.33b 1619
 Description: The antecedent provides a condition implying the converse of 19.33 1618. Compare Theorem 19.33 of [Margaris] p. 90. (Contributed by NM, 27-Mar-2004.) (Proof shortened by Andrew Salmon, 25-May-2011.) (Proof shortened by Wolf Lammen, 5-Jul-2014.)
Assertion
Ref Expression
19.33b

Proof of Theorem 19.33b
StepHypRef Expression
1 ianor 476 . . 3
2 alnex 1553 . . . . . 6
3 pm2.53 364 . . . . . . 7
43al2imi 1571 . . . . . 6
52, 4syl5bir 211 . . . . 5
6 olc 375 . . . . 5
75, 6syl6com 34 . . . 4
8 19.30 1615 . . . . . . 7
98orcomd 379 . . . . . 6
109ord 368 . . . . 5
11 orc 376 . . . . 5
1210, 11syl6com 34 . . . 4
137, 12jaoi 370 . . 3
141, 13sylbi 189 . 2
15 19.33 1618 . 2
1614, 15impbid1 196 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 178   wo 359   wa 360  wal 1550  wex 1551 This theorem is referenced by:  kmlem16  8050 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-ex 1552
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