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Theorem 19.33b2 1520
 Description: The antecedent provides a condition implying the converse of 19.33 1373. Compare Theorem 19.33 of [Margaris] p. 90. This variation of 19.33bdc 1521 is intuitionistically valid without a decidability condition. (Contributed by Mario Carneiro, 2-Feb-2015.)
Assertion
Ref Expression
19.33b2

Proof of Theorem 19.33b2
StepHypRef Expression
1 orcom 647 . . . . 5
2 alnex 1388 . . . . . 6
3 alnex 1388 . . . . . 6
42, 3orbi12i 681 . . . . 5
51, 4bitr4i 176 . . . 4
6 pm2.53 641 . . . . . . 7
76orcoms 649 . . . . . 6
87al2imi 1347 . . . . 5
9 pm2.53 641 . . . . . 6
109al2imi 1347 . . . . 5
118, 10orim12d 700 . . . 4
125, 11syl5bi 141 . . 3
1312com12 27 . 2
14 19.33 1373 . 2
1513, 14impbid1 130 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 98   wo 629  wal 1241  wex 1381 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 630  ax-5 1336  ax-gen 1338  ax-ie2 1383 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-fal 1249 This theorem is referenced by:  19.33bdc  1521
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