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Theorem 19.33b 1595
 Description: The antecedent provides a condition implying the converse of 19.33 1594. 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 474 . . 3
2 alnex 1530 . . . . . 6
3 pm2.53 362 . . . . . . 7
43al2imi 1548 . . . . . 6
52, 4syl5bir 209 . . . . 5
6 olc 373 . . . . 5
75, 6syl6com 31 . . . 4
8 19.30 1591 . . . . . . 7
98orcomd 377 . . . . . 6
109ord 366 . . . . 5
11 orc 374 . . . . 5
1210, 11syl6com 31 . . . 4
137, 12jaoi 368 . . 3
141, 13sylbi 187 . 2
15 19.33 1594 . 2
1614, 15impbid1 194 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 176   wo 357   wa 358  wal 1527  wex 1528 This theorem is referenced by:  kmlem16  7791 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-ex 1529
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