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Theorem 19.33b 1696
Description: The antecedent provides a condition implying the converse of 19.33 1695. (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 1614 . . . . . 6
3 pm2.53 373 . . . . . . 7
43al2imi 1636 . . . . . 6
52, 4syl5bir 218 . . . . 5
6 olc 384 . . . . 5
75, 6syl6com 35 . . . 4
8 19.30 1692 . . . . . . 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 1695 . 2
1614, 15impbid1 203 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  <->wb 184  \/wo 368  /\wa 369  A.wal 1393  E.wex 1612
This theorem is referenced by:  kmlem16  8566
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-ex 1613
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