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Theorem 19.33b 1697
 Description: The antecedent provides a condition implying the converse of 19.33 1696. (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 488 . . 3
2 alnex 1615 . . . . . 6
3 pm2.53 373 . . . . . . 7
43al2imi 1637 . . . . . 6
52, 4syl5bir 218 . . . . 5
6 olc 384 . . . . 5
75, 6syl6com 35 . . . 4
8 19.30 1693 . . . . . . 7
98orcomd 388 . . . . . 6
109ord 377 . . . . 5
11 orc 385 . . . . 5
1210, 11syl6com 35 . . . 4
137, 12jaoi 379 . . 3
141, 13sylbi 195 . 2
15 19.33 1696 . 2
1614, 15impbid1 203 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 184   wo 368   wa 369  wal 1393  wex 1613 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-ex 1614 This theorem is referenced by:  kmlem16  8562
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