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Mirrors > Home > ILE Home > Th. List > 19.33b2 | Unicode version |
Description: The antecedent provides a condition implying the converse of 19.33 1477. Compare Theorem 19.33 of [Margaris] p. 90. This variation of 19.33bdc 1623 is intuitionistically valid without a decidability condition. (Contributed by Mario Carneiro, 2-Feb-2015.) |
Ref | Expression |
---|---|
19.33b2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | orcom 723 | . . . . 5 | |
2 | alnex 1492 | . . . . . 6 | |
3 | alnex 1492 | . . . . . 6 | |
4 | 2, 3 | orbi12i 759 | . . . . 5 |
5 | 1, 4 | bitr4i 186 | . . . 4 |
6 | pm2.53 717 | . . . . . . 7 | |
7 | 6 | orcoms 725 | . . . . . 6 |
8 | 7 | al2imi 1451 | . . . . 5 |
9 | pm2.53 717 | . . . . . 6 | |
10 | 9 | al2imi 1451 | . . . . 5 |
11 | 8, 10 | orim12d 781 | . . . 4 |
12 | 5, 11 | syl5bi 151 | . . 3 |
13 | 12 | com12 30 | . 2 |
14 | 19.33 1477 | . 2 | |
15 | 13, 14 | impbid1 141 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wb 104 wo 703 wal 1346 wex 1485 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 609 ax-in2 610 ax-io 704 ax-5 1440 ax-gen 1442 ax-ie2 1487 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-fal 1354 |
This theorem is referenced by: 19.33bdc 1623 |
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